To be honest, and speaking purely unofficially, if I were going to tag my own fic, I would only use "polyamory" on fics about modern people who self-identify as poly. I wouldn't use it for most multi-person or non-monogamous relationships that happen between people who either don't identify that way in the modern day (cheaters, swingers, orgy participants) or who aren't from the same cultural background as poly-the-identity (aliens, characters in Ancient Rome).

My feeling is that the "Multi" description currently implies that it's for fics with some mix of m/m, f/f, and m/f pairings ("more than one kind of the relationships listed here") and that "Other" refers to relationships that are not neatly categorized as m/m, f/f, m/f, or any combination of those. Whether that's how everyone would interpret those and whether those are the best options to have, I couldn't say.