Rune Factory: Tides of Destiny starts out with two characters, a brother and sister. You can play as male or female, but thanks to a magical accident, the other sibling will co-habit their twin's body near the beginning of the story. Both siblings can date bachelor/ettes, but the system only corresponds to "hetero" relationships. I guess, technically, the host body could be considered polyamorous? I haven't played more than a chapter or two into the storyline, however, since the only copy available to me is a library rental.
I also enjoy interactive novels, the "choose your own adventure" stories. Usually, you can play as male, female, trans, non-binary, gay, straight, bi, or ace. However, the romantic interests in most of these games seem to be constrained to one or two character archetypes, which I find rather boring. Other than that, I don't know much more about LGBT representation in video games.