Spot-on!
GC people have been getting away with ugly attitudes for far too long based on a premise that isn't adequate to support their perspective.
Rather than going after the sex-is-binary premise (which is difficult--most trans advocates start off getting it wrong, as do most gender crits), going after the reasoning from the premise is exactly the right call, I think, because that is the part that is really hurtful.
Also, I advise you not to add "segregation for sport" in this article. This is really nice as it is: it takes a very strong statement from GCs that denies the validity of every trans person, and demolishes their argument in the general case. (They could come back and argue specific cases, but voiding the general principle is the key contribution here.)
This is so focused and compelling as it is that I hope you tackle related topics in additional articles rather than amending this one.