"Old Internet" doesn't have a very defined meaning, but I think it has more to do with design and functionality than a hard date. While I don't think relevance matters, 4chan is much more relevant than you think. Having a niche is part of the old Internet. Websites used to be niche, but deep, instead of websites like Wikipedia, which are broad and shallow (compare the Castlevania dungeon [0] to the Wikipedia article for Castlevania, for example). Then compare 4chan's limited number of boards with reddit's endless subs. 4chan's design is early web 2.0, doesn't require you create an account, allows (pseudo) anonymous posting, content is mostly unfiltered, unmonetized, free & thought of as ephemeral, etc.
0 - https://castlevaniadungeon.net/dungeon.html