You caught the "friend" part, right? Like the article you linked said, a lot of people without malicious intentions buy into this rhetoric because it seems correct intuitively. And after reading the study, it's not completely baseless to say trans women have an advantage over cis women in some cases.
I found this bit to be particularly interesting: "Furthermore, two transgender women and one cisgender woman were excluded from all analyses due to testosterone concentrations exceeding recommended female testosterone concentrations (2.7 nmol/L15)."
I'm sure y'all know it's a thing that some cis women have higher testosterone than is typical for women, and it certainly affects performance. I bet those women are overrepresented among professional athletes. Is that "fair" to women who have naturally lower and more typical levels?
The big advantage that trans women seem to have, based on this study, is their larger than average size. The article mentioned they have better grip strength, but the study says they don't if you control for hand size. So it's just a matter of them having larger hands on average. Again, plenty of cis women are bigger and taller than average, and they're probably overrepresented in sports where that's an advantage.
On the face of it, it seems like maybe sports should be segregated by testosterone levels and body size rather than gender. It does leave the question of where people who are above average in one and not the other should be grouped though.