As far as I can tell from a brief look at the paper, it makes no attempt to estimate whether the increased fecundity of the female relative is enough to compensate for the reduced fecundity of the homosexuals. In fact, I didn't see it give any estimate for the latter. They merely do a p-test and pronounce the differences "significant". This is a situation where we are primarily interested in the magnitude of the effect, not merely finding evidence that it is positive.
Right--as well, the standard complaint about extending this logic to humans is that the most credible increased fertility effect for female relatives is desire-based. But it's easy for women to get pregnant more frequently and have more children--the hard part is keeping those children fed until they're self-sufficient, and dividing your wealth among all your children, neither of which it seems gay uncles help with enough to explain the effect.
Epistemic status: speculating about things I'm not familiar with; hoping to be educated in the comments. This post is a question, not an answer.
ETA: this comment thread seems to be leading towards the best answer so far.
There's a question I've seen many times, most recently in Scott Alexander's recent links thread. This latest variant goes like this:
Obligate male homosexuality greatly harms reproductive fitness. And so, the argument goes, there must be some other selection pressure, one great enough to overcome the drastic effect of not having any children. The comments on that post list several other proposed answers, all of them suggesting a tradeoff vs. a benefit elsewhere: for instance, that it pays to have some proportion of gay men who invest their resources in their nieces and nephews instead of their own children.
But how do we know if this is a valid question - if the situation really needs to be explained at all?
For obvious political and social reasons, it's hard to be sure how many people are homosexual. Note that we are interested only in obligate homosexuality - bisexuals presumably don't have strongly reduced fitness. The Wikipedia article doesn't really distinguish obligate homosexuality from bi-, pan- and even trans-sexuals. The discussion in the SSC comments used an (unsourced?) range of 1%-3%, which seems at least consistent with other sources, so let's run with that.
The rate of major birth defects in the US, as reported by the CDC, is also about 3%. This counts both developmental and genetic problems, and includes everything from anencephaly (invariably fatal) through Down syndrome (severe but survivable) to cleft palates (minor). But most of these, at least 1.5% of births, were always fatal before modern medicine, and many of the others reduced fitness (via mate selection, if nothing else). Various other defects and diseases, which only manifest later in life, are also thought to be influenced or determined during early development. And so is sexual preference.
(Whether homosexuality is a developmental disorder is not the point; I'm comparing the effect of selection pressure on fatal teratology with its effect on reduced-fitness homosexuality.)
Embryological development is a complex and fragile process, and there are many ways for it to go wrong. We don't wonder how it is possible that selection pressure allows anencephaly to occur in 1 in 4859 births. There are certainly direct causes of anencephaly, explanations of why it happens when it does, but (I think) we don't a priori expect them to be due to tradeoffs yielding benefits elsewhere. It's just as plausible that the tradeoffs involved are against even worse (counterfactual) problems elsewhere - or that there are just no available mutations that don't have these or equally severe problems.
Could it be that linking sexual preference to the biological gender is, for some complex developmental reason, fragile enough that it goes wrong despite all selection pressure to the contrary, that it has no redeeming qualities from the viewpoint of evolution, and that is all there is to it?
When faced with any phenotype with reduced fitness, how can we judge if there is something to be explained - a beneficial tradeoff elsewhere to search for - or merely a hard problem evolution couldn't solve completely? And is there a way to quantify this question, relating it to the known mathematical models of genetics?
Notes:
1. I'm posting this in the spirit of recent suggestions to post more and accept lower quality of (our own) posts to Discussion.
2. I'm going to sleep now and will start replying to comments about 10 hours from now; sorry for the inconvenience.