I usually only see them use “they/them” when referring to MC since MC can be either gender while established characters are given gender-specific pronouns unless the character is non-binary. Or when the story is referring to the match character as “they/them”, which I don’t really mind.
It may be the case that Lovelink was programmed to have all pronouns referring to both MC and the match outside of dialogue/chats to be gender neutral so that they wouldn’t have to be manually edited for each character to keep things simple for the writers and/or programmers.
I did see William refer to their fiance as “they/them”, but I don’t really mind it in cases like that and it’s probably to leave the sexuality of the character more unknown and open than if the writers had assigned a gender. I wouldn’t have minded that either, but I see what they may have been going for by not doing so. I’m fine with it being either way, personally.