For what it's worth, the only mystery about Izuki's gender is what exactly caused the change. There was definitely a physiological change, though, if you re-read the start of chapter 2:
Doctor: It's quite frequent for a person to have gender identity confusion when they reach puberty.
Izuki's mom: Well...actually...it's not confusion but his gender has changed...
Also, Ritsu's wish seems like it actually happens after the gender change has started. He says in chapter 1 that he won't be able to play in the finals, which is the game where Izuki gets her first period, and the end of chapter 1 and the beginning of chapter 2 establish that the Fujiwara family was aware of the change before that point, which makes sense, since Izuki was going to tell Ritsu about it at the airport.
There's still room for Ritsu to have misplaced guilt over a wish that happens to fit the situation, or for the wish scene to have happened earlier than it seems, but based on the story so far I don't think it had anything to do with it.