I can certainly see how it could be a relief not to think about how to “justify the ways of God to man,” as Milton put it. But how is this connected to “what atheism has to offer”? What does atheism have to offer when “a loved one [is] losing his mind to Alzheimer’s,” and so on? I don’t see how atheism qua atheism (as the philosophers say) has anything at all to offer, though particular atheists, just like particular religious believers, can certainly offer a lot in the way of care, compassion, physical and emotional assistance.I think the best way to think about this is in terms of balance. A religious person, upon facing the horrible fact of a loved one's imminent demise, has to balance their belief that their family member is going to be released into Paradise very soon, and their confusion as to why a supposedly loving God would allow such suffering in the first place. The force here that actually tips the scales varies from person to person, but it seems relatively uncontroversial to argue that for some people, the confusion is so much more pronounced that they might be better off without it, even at the cost of losing their comfort over approaching Paradise.
Even if that doesn't hold, once we reach Susan Jacoby's original example of someone suffering horribly but in no imminent danger of death, the calculus becomes pretty easy: not having to ask questions of why your love one was specifically picked is an advantage. And that's an advantage that atheism offers. The fact that it doesn't actively offer it through an agreed upon theology is beside the point. Atheism qua atheism (as the philosophers and bloggers say) offers the advantage that it has none of the downsides of religion. If a pilot has a heart attack on a plane, and the only passenger who isn't entirely blind has no experience of flying, there's still an advantage in picking her to be the one to give landing a go.
Jacoby seems to be saying that atheism can have a role in an atheist’s life that’s similar to the role religion has in the life of a religious person, but I can’t see how that could be so. A religious person might say, “I help those who suffer because I believe that God wants me to do that,” but I don’t imagine that an atheist says that helps those who suffer just because she is an atheist.This is somewhere between a logical fallacy and a failure of imagination on Jacob's part, trying as it does to consider the motivations of people who lack any other features other than their religious or non-religious views. If there's one thing someone who writes for the American Conservative should have picked up on, it's that there are plenty of self-professed Christians who demonstrate absolutely no outward sign whatsoever that they desire to help anyone other than themselves. Yes, it is something they are supposed to do, according to what most people would consider basic Christian tenets (though there's always someone willing to argue that a given central theological assumption is actually incorrect; that's why the church had to come up with the idea of heresy). That does not mean nominally Christian people will not go out of their way to avoid doing so. Some, like Paul Ryan, actually create complex (and utterly disgusting) philosophies to portray their selfishness as high-minded altruism. Others, like Rush Limbaugh, are just gangrenous pricks.
So Christian => empathic doesn't follow automatically. Neither does atheist => empathic, which is what Jacobs is objecting to regarding Jacoby's article. But if Jacobs gets to use common acceptance of a well-established point in his favour, then so do we. The argument that Jacoby not only uses, but Jacobs himself quotes later in the article, gets us most of the way: if there is no afterlife to reward people who suffer in this world, we should work towards alleviating suffering in the only lives we have. 
Like many other people with depression, I am prescribed medication with unwelcome side-effects. They're not too bad in general, but if I forget to take my pill at roughly the same time every day, or when I start up the medication again after a period of trying things chemical-free, I'm prone to horrible panic attacks and nausea. I suffer these things because my doctor tells me that once I'm passed the burn-in period (and if I can settle into a routine), my life will significantly improve. And, to be fair, they were right.
But what if I believed they were wrong; that the side-effects of the pills are the only effects. Wouldn't that make me want to actively avoid the pills? Wouldn't that make me want to ensure other people avoided them?
The counter here of course is that there's a leap between "I want to stop taking the pills because there is no reward in doing so" and "I want to help other people stop taking the pills because there is no reward in doing so". Like I say, though, that leap exists for Christians as well, even though theologically it shouldn't. Christianity says helping people is good because it's what God wants. Atheism says helping people is good because this is all there is, and it shouldn't suck if we can help it. Whether or not people choose to act on those impulsions (and note that I'm not arguing that they are necessarily equally powerful) is down to the individual. When Jacob argues "“There is no God and therefore I should be compassionate” is a syllogism with evident missing parts", he's not wrong, but he's neglecting to consider that "There is a God and therefore I should be compassionate" is in itself incomplete, it's just the missing parts have become sufficiently internalised by his religious organisation that the gaps no longer register.
In short, atheism does not force people to care about others, but any atheist who cares about others can sensibly describe how their atheism plays into their empathy. Similarly, Christianity cannot force people to care about others (though it perhaps has the edge in compelling people to pretend otherwise), but empathic Christians have no problem using their theology to explain why they want to be who they are.
 A quick anecdotal aside; a few years ago I had a conversation with a good friend and several other members of her church about the potential benefits of Christians and atheists working together in putting together charitable entities and events. The general feeling around the table was that this wouldn't be a good idea, because of incompatible goals. In other words, helping people for their own sake couldn't be the only goal for those particular Christians. I'm not saying this is in any way representative of Christianity in general, I'm just pointing out that it is possible to construct a situation in which Christian objectives - in this case a strong commitment to evangelism - can actually work against the desire to help others, a problem which atheism does not suffer.