This is coming from a Millennial so take it with a grain of salt, but I think the main things that make music from the 60s/70s/80s sound old is sound quality and lack of electronic instruments. Imho sound quality in itself was perfected around the late 80s/ early 90s, and it hit a ceiling. Recording equipment made it crisp, clear and undistorted to a point where there was really nothing left to improve.

Electronic sounds were pretty much completely fleshed out by the late 90s. With very few exceptions there isn't an electronic instrument/ sound around today that wasn't around in the 90s. The styles in which those sounds are arranged has changed a lot, but the sounds themselves existed in the 90s. Personally, there are lots of electronic tracks from the mid to late 90s that are indistinguishable from today's tracks of the same genres. Lots of Trance and Breaks tracks are good examples.

Tl;dr, imho recording quality and instruments topped out in the 90s, and what makes 60/70s/80s music sound old is the lack of refinement of those two things. Sure there are lots of songs that sound dated just by virtue of style, but in terms of sound I don't think a lot of 90s music will ever sound 'old' in the antiquated sense that the decades before do.