Xbox Live was a year late, and has since been shut down regardless. Phantasy Star came with an online adapter for GameCube, but I think that was for Japan only, and GCN came out the same fall as THPS3 for PS2, maybe even a few weeks later. And I imagine PSO itself no longer works on the Cube anyway.
Online handhelds didnt quite exist, there may have been a Tiger Electronics toy predating Tony Hawk 3, but no way it still works today. And of course you can still play Doom/Quake/Unreal/Counter Strike on PCs, though those are heavily patched to work today, and consist of remakes like Quake Live.
Dreamcast predated this, but I havent heard whether that still connects to the internet. I remember it using a proprietary AOL style dial up service from AT&T.
So is THPS3 for the PS2 the oldest, unmodified, unhacked, un-remastered (console?) game you can still play online?