You're not really missing much. As the saying goes, there's not a lot of there there.

To back up, epigenetics is the study of how genes are expressed (loosely speaking). Chromatin, the stuff that's actually inherited, contains many more molecules than just DNA. The way these other molecules are arranged or bound to the DNA can influence which genes are expressed when and in what quantity.

Their hypothesis is that exposure to a specific hormone, androgen, during gestation causes changes in developing embryos that influence sex development. Apparently, heightened androgen exposure can make females seem more male and males seem more female. However, even identical twins react differently to androgen in utero, where one would expect the environment to be identical. Therefore, the differences in sensitivity to androgen or other influencing factors is probably due to epigenetic differences in the embryos. They then make a huge leap to say that the prevalence of homosexuality and its seeming heritability resemble (mathematically speaking) the ways in which epigenetic traits are passed on. Putting all this together, they are proposing (I think) that homosexuality results from a combination of epigenetic and environmental factors.

This doesn't sound unreasonable per se, but their evidence is not close to convincing. Sounds like a reach, but it's provocative, so maybe it will start a decent conversation on the topic. Personally, I think it's dangerous to try to find a genetic mark for homosexuality. Firstly, what if this marker does exist? Would parents be allowed to abort if they thought that being gay was abnormal? Second, what if your kid insists they're gay, so you test him/her for "the gene". They come back negative, so then what, you send them to a counselor to convince then they aren't gay even though they feel that way? Genetic testing fro personality traits is ostensibly a way to "legitimize" the trait, but I think it's a subtle form of oppression and fatalism. But that's just my editorializing, nothing to do with the paper itself.