Personally, I don't think so. Just because Super Mario Bros. 2 features a trans character, it doesn't give the game explicit trans themes. Games like Rocky Horror Show, on the other hand do. So, should we clean the list of games that only contain characters which are LGBT, but do not mention gay themes  specifically?

The category simply states the game includes a LGBT character, not that the game is solely based around this character. So, no.

Yeah, we're not really talking about the game having explicit LGBT themes, the article is just stating the games that LGBT characters appear in in whatever nature.