Well, first I must congratulate you. I love the game's premise and I love the demo so far. I'm glad you're not upset about the scores they gave you, because you really shouldn't, the game is amazing.
As for the things they've accused you:
Well, I'm white, so although I haven't seen anything racist, it's not up to me to say, so I'll focus on the supposed transphobia.
At the beginning, surely many people can be confused about the Queen. Call a queen "he" may sound at least strange at first, but when we get our roles it's clear that the characters' gender doesn't matter for what role we get, so it's perfectly fine. I was thinking of suggesting you write "they" or just avoid using pronouns at the first part of the game, but after a while it's clear that the Queen is a man, we get to see that, not a transwoman or any other gender than male. So maybe you could just add some thing that suggests you know that the Queen is a man, something that suggests that you've met him before. It's not that important, however, it can just stay as it is.
The game is well written but it has some words I find a little too complex to my understanding of English, so I can't say I have understand fully all the phrases. One of them is this one: The King takes the White Queen's hand and kisses his knuckles, and you can't help but feel the mockery in the gesture; his wide movements, slow and deliberate, scream of travesty. His, whom? The Queen or the King? Scream of travesty? I don't really get it, but as "travesty" may be a delicate word for some people, maybe it would be better to change it, but I don't know.
But is this transphobic? Hell no.
Honestly, very much the opposite: you don't have idea how surprised and happy I got to see that I wouldn't have to write my gender myself, it was on the gender selection already, together with many others n-b genders, plus the option to choose pronouns, not being obligated to go by the standard they/them. Your game is in fact one of the most inclusive games I've ever seen with non-binary trans people.
All the stuff that I mentioned above about possible "transphobic" scenes aren't transphobic at all, I just can't see how this could be seen as transphobic if not by misreading.
As for homophobia, I really didn't find any clues. I have no idea what could have bothered the judges so far.
I played the game being part of the White team, so maybe there's some more stuff I didn't see yet. Maybe I'll try playing being part of the Black team later.
But that's it. I'm n-b, pan, I'm loving it and didn't feel offended AT ALL.
so, uh, what does "finespun" mean? I couldn't find a translation for this word. Judging by its opposite, I assume it's something like "well disguised", is that right?