You're right, Polyamory would technically be more appropriate. Polygamy generally refers to 'Marriage', but it is also is more associated with a man taking multiple female partners. Where as Polyamory could imply males with males and females with other males. I don't want people thinking there could be NTR in Avalon because there's not. But you're technically right.
I'm not sure where you get that polyamory implies gay or NTR content. Polyamory is simply having a consensual open relationship with more than two partners. I know many straight hetero poly folks. Polygamy, on the other hand, is illegal in the US (although Utah has managed to reduce the severity of it, it's still illegal), whereas polyamory is not. The unfortunate reality is that many people are misinformed to believe that the two terms mean the same thing, and they very much do not. As someone who's been poly for more than twenty years, and has been involved in sex education for about as long, I lean towards correcting folks when they get the two mixed up.
I know of several developers who have been very clear that their games do not contain NTR, even when the tag is not there, for similar reasons. That might be a direction you would wish to pursue. I've played the game, and while I do enjoy it, the incorrect terminology tends to put me off every time it comes up.