Polygamy does mean marriages but has been missed because people didn't have better alternative words. "Menage a trois" is another term not needing marriage but has connotations to some of being mostly sexual and also only cover 3 people.
Polyamory as a word wasn't really widely used until the 90s and it's only really become mainstream in the last maybe 10 years?
Polyamory is much more precise and correct than polygamy.for describing relationships outside marriage. Polygamy is also a legal term very specifically related to marriage laws.