I'm guessing you missed the part where they specifically talk about using only facial structure (nose, jaw shape, etc) and still getting good results? They even talk about there being a long-standing theory predicting the differences they found...
If you look at the facial landmarks figure[1], it seems that the main difference between a "gay" and a "straight" man is how fat/thin their face is. Maybe gay people are on average less overweight? That's possible, but that's hardly an intrinsic characteristic. Eyebrow shape is not intrinsic either.