No, I do not.
https://www.merriam-webster.com/dictionary/trigger%20warning
Gay parents are not disturbing or upsetting content.
You are not understanding, and I fully realize that you will likely not in a conversation with me. Should readers be "notified" about heterosexual parents too? I suspect your answer is 'no.' That is my issue with what you are suggesting. I will not treat parents with non-hetero orientations any differently in fiction or in real life. End of story.
I understand you. I personally have nothing against indicating the heterosexuality of parents in the description. So your reluctance to point this out seems...strange to me. But do you realize that leaving the description of the game so vague as it is now can also lead to other people like me who will wander into your game when the content in it is not for them? In my opinion, you will win in the long run if you make the description more transparent. Well, it's up to you in the end, I just wanted to give you reasonable advice for the description, nothing more really.
The point I'm making is that you only take issue if the parents are gay specifically. I am saying parents are parents regardless of sexuality. Neither is beholden to being warned about anywhere. The description doesn't need to be "more transparent" in that fashion. The strange thing here, is that you do not seem to realize how homophobic your "advice" is. If one would not notify about straight parents, one would not notify about gay parents either.
The story isn't even about the MC's parents, they're a supporting role. There is no content to even warn about, it's a non-issue that you have a problem with due to prejudice. Your "advice" is not reasonable, it's bigoted and therefore unwarranted and unwanted.
You aren't understanding that no one wants people who think like you playing this game. If you are triggered by gay parent's any lgbt tag games aren't for you because you guessed it! People in the lgbt space will play them and they don't give a damn about what you are whining about just like we wouldn't give 2 shits about if the parent's were straight. But you don't see us demanding trigger warnings for straight parents in other books.
Go try find a hetero based christian game or some shit. Hopefully they have gender selection for you. Some mcs are gay too that's the whole point of a game where you can choose your gender and your ROs. Must be the gay dad's that inspired us.