Fucking hell, that's one of the worst-written papers I have ever read - can't believe that it got published in Nature.
Basically, they used MRI scans to compare the size of various brain components in 4 groups: men, women, TIM before hormone treatment and TIM on hormone treatment. There are loads of potential flaws in their methodology: the groups studied were very small, for example, and it's not clear that the scientists assigned to analyse the MRIs were blind to (unaware of) which group each patient came from - so there is a high risk that they weren't objective.
More fundamentally, though, their hypothesis doesn't fit their own data. They seem to be saying that there are innate biological differences between biological men and TIM, and that TIM are on a spectrum between bio men and bio women. If this hypothesis were true, you would expect the pre-treatment TIMs' results to be somewhere between the bio men and bio women. But that's not what they found: where they give the results of a direct comparison between the 4 groups, the differences between the pre-treatment TIMs and bio women are actually greater than between bio men and bio women, in most respects. So, if anything, the TIMs are more masculine than the bio men! The hormone-treated TIMs are a bit more like the women than the pre-treatment TIMs, though not very. What this suggests is the exact opposite of their hypothesis: there are no innate differences between TIMs and other men, but taking female hormones (not surprisingly) may have some effect on the brain.
In most cases, though they avoid a direct comparison between the 4 groups, but just give comparisons between two groups at a time and without the actual data: they just tell you that one group had a bigger brain component than the other. This is highly suspicious. I can't think of any reason for not giving the raw data than that it would have further undermined their hypothesis.