Exactly my thinking! I'm a trans male and it just feels odd and a bit degrading not to have an option for he/him pronouns.
I think since the game is categorized as an "otome", the creator most likely wouldn't add he/him pronouns! (and also because it'd be quite time consuming to tailor the scenes again) Otome games are targeted primarily towards a female audience, instead of the opposite or other (take Love and Deepspace as an example). Though, there are plenty other games like/similar to this with other pronoun options !