"Therefore, just as sin entered the world through one man, and death through sin, and in this way death came to all people, because all sinned." Romans 5:12(Who spoilers from jump)
I suppose it's only appropriate, given how evocative this episode was of classic Who adventrures (the confrontations between the Doctor and the Fisher King reminded me of "Curse of Fenric" in particular) that this episode feels like it belongs to an earlier season. Not necessarily much earlier, but this feels very much like an Eleventh Doctor story. In particular - obviously - the Eleventh Doctor story "The God Complex" (itself tremendously "...Fenric" in structure, of course), right down to the TARDIS being unable to escape the situation that has developed. I say "obviously" since they share a writer, but it's far more than just that. The Fisher King, like the Nimon that (sort of) appeared in that earlier episode, is a creature from our myths. Of course, in the case of the Nimon, the suggestion is that they literally pushed their way into our myths as a method of dominance (the relative in "The God Complex" took this a stage further and literally fed off the belief such an incursion could generate). Here, it appears the Fisher King is simply named after a figure from Arthurian myth, with no greater link than that. At best, a name simply applied for the sake of some potential Arthurian connection throughout the season (we've come across Bors already, of course, probably better known these days for being decapitated by a rabbit than his actual legendary exploits), at worst it was just chosen at random because it sounded cool, and because also I guess because lakes.
But is that really true? A wounded king, waiting for someone who can heal him? An impotent ruler, unable to further his line, casting his nets whilst he waits for release? There's more of a little of that here, I would think. Our Fisher King is certainly wounded, to the point where the Tivolians believed him dead. And, like the classic Arthurian model, our King is helpless to aid himself without someone coming to heal him. Of course here, the healing comes not from actual medical aid, but from the fact that without more people, he has no hope of generating the message he need to effect rescue (and perhaps greater healing); the fish he hunts and the rescuers he awaits are the same thing. Note how he plays possum until the Doctor, O'Donnell and Bennett arrive - the magic he needs to "heal" himself (which he gets from a doctor, of course) can only come from other souls in sufficient bulk. When you are impotent, all you can create is corpses.
(Note what he does with those souls, by the way; he kills them and resurrects them without the ability to speak. That is exactly what Bran the Blessed - considered the inspiration for the Fisher King myth - does in the Mabinogion, uses his magic cauldron to bring people back from the dead at the cost of their voices. If there is literally nothing else in the episode that explains the alien's name, this alone would drag it past the point of randomness.)
That for me is enough to justify deploying the mythological name, but in addition you have the idea of the Fisher King trapped in the past. What other reason can there be for the decision to set his death in 1980 rather than 2015? Other than the fact that it means I could theoretically be the reincarnation of FK, I guess, which honestly might explain a few things. But the point is that the King isn't of the present, he is of the past, and a past that never unravelled the way people assumed it would. Setting these sequences in a town built to provide troops with experience of Soviet-era Russia underlines the point; just like the threat of the Fisher King awakening from the pale tomb inside the Drum, the Cold War never turned hot. Every moment of preparation troops spent learning to fight the Russians was in service of a war that never ignited. Ultimately, the Cold War was a story, no less surely a myth than the one about the king who waited for Sir Gawain. And yes, it was a story that killed who knows how many people and resulted in the misery of who knows how many more. It was far from the only story to do colossal damage. That's why good stories are so important; they crowd out the dangerous ones.
(On the subject of the pseudo-Russian village, let's just take a moment to marvel at how absolutely lovely the '80 location looked. If the aim of this brace of two-parters was to save money, the absolute brilliance of both the abandoned town - all faded colours and dusty decay - and the Fisher King himself suggests at least someone didn't get the brief. I mean, seriously, the Fisher King is just wonderful. Jack Graham is absolutely right when he calls them a cross between a Vervoid and an ID4 alien, but that fails to get across that both those designs are awesome (yes, even the fact the Vervoids heads are clearly clitorises) and their combination here is better than either.)
With his name explored, let's consider the role the Fisher King takes here. The explicit point of "The God Complex" was that the Doctor and the creature were dark images of each other - the Doctor uses faith just as surely as his opponent did, and death still ends up being the end result. The degree to which that critique actually lands is a topic for some other post, but with so much here being reminiscent of Whithouse's earlier effort, should there not be some kind of twisted mirror effect going on between Doctor and King?
Well, on the most simple rhetorical level, of course, there is: the Fisher King will sacrifice lives to extend his time alive (or at least relevant; it's not clear if he's actually dying here), whereas the Doctor will risk sacrificing time in order to save lives. Except... that's not completely true, is it? Bennett's argument that the Doctor was willing to sacrifice O'Donnell to test a theory he could use to try and save his own life  certainly has more than a ring of truth about it. Sure, the Doctor is leaping into action in order to save Clara rather than himself, but Bennett's point is no less powerful for that. And the episode's resolution makes the accusation even more powerful. Hand-waving about the Bootstrap Paradox notwithstanding, what was there to stop the Doctor listing Clara ahead of O'Donnell and thereby probably saving her life? Was testing his theory really that important? Was he worried that he wouldn't risk the ripple effect if he wasn't sure Clara was about to die? The idea of the time-loop here serves to implicate the Doctor further, it's not just that he was willing to use O'Donnell as a test case for this theory, it's that he knew he was going to be willing to use O'Donnell that way. In that sense, O'Donnell's death is used to send a message to the Doctor just as surely as the Fisher King uses his ghosts to beam his coordinates to the stars.
(Speaking of coordinates; it's unquestionably true that using the constellation of Orion as a signpost is utterly deranged; even if the three stellar bodies that form the sword actually form a three-dimensional line, we clearly couldn't be on that line. Beyond that, though, no-one from off Earth would understand the reference, and anyone from even a little away from us (speaking in interstellar terms, of course) wouldn't see the constellation in remotely the same way as we do in any case. Some of this is mitigated, though, if the Fisher King or other members of his race have been here before, resurrecting the silent dead for their own purposes. When Prentis refers to Earth as a remote outpost, does he mean that from the perspective of the Tivolians, or their conquerors? Surely it's almost certainly the former; it's hard to imagine the Tivolians setting up interstellar colonies, at least on worlds which lack the ability to travel en masse back home to get some proper oppression going. So I think it's pretty clear that the Fisher King's race have been to Earth before, specifically Wales.)
Unlike the ludicrous accusations levelled at the Doctor by Davros in "Journey's End", this kind of objection, that the Doctor's decisions are massively dependent upon who will be affected, are utterly justified. I mean, one could simply respond that this is how fiction works, but that doesn't change the fact that it's true, and in any case the problem of rewriting our thought processes whenever our own people are affected is sufficiently deep-rooted and harmful within humanity that I think it bears repeating how thoroughly it's baked into our stories as well. I keep coming back to Romans 5:12. It's almost certainly totally coincidental that the TARDIS obscures the number 512 as it returns to the windswept town, but it got me thinking. There's actually some relevance to the Biblical passage here, once you think of reading the Fisher King's carvings as sin, or more accurately, as the realisation of sin, as I argued last week we should (with both episodes done, we can now be sure that every character killed by the ghosts or the King himself were white). And with the TARDIS effacing the number with its arrival, the temptation would be to believe that the Doctor has arrived to break that cycle, that the deaths will finally stop.
But it isn't that simple. The camera moves, and the number is back. The Doctor passes directly underneath it. If the basic accusation of "The God Complex" is that sooner or later the Doctor brings death to his people, then there is much here that is grist for the mill (and while we're on the subject, am I supposed to fucking care that if you tell Prentis about what's happening it will be weird for you? Am I supposed to believe that somehow your fear about seeing ghosts is somehow more important than Prentis' life?). The Doctor might be dedicated to saving people from the deadly threats of the universe, but he brings his own death right along with him. His own sin.
This is why I say this story would have been better placed a few years ago. Not just because the assumed destruction of Gallifrey would have given the Doctor and the Fisher King one more parallel of being unable to create anything but death (for all that even with the Time Lords running around the only Doctor to show any interest in a bit of horizontal time-jogging was the Fourth), but because his status at the time as the architect of his own race's genocide would have underlined just how much death the Doctor was dragging along on his coattails.
With us entering the story of the girl who died, that's perhaps something worth remembering.
 Note, by the way, how the episode works to drop hints about the resolution. The Doctor's image chants the names of the dead exactly according to how he and Clara knew them - why else would he use the surnames of the base crew but not refer to Clara as "Oswald"? There's also the mystery of why the Doctor's ghost appears before O'Donnell's.