Saw this FB post at the time of writing this (https://www.facebook.com/PlayParkPHINC/posts/pfbid02aXgCREpLtM45hsGPuANgLxZZvikZtQdotCmFhPjEMLEbD1XnB4jki8jA3csH27KTl) and well, why not make a list from it, and maybe add some additions to it since we used to operate an internet cafe before.
Limited to games that are online, can be played through LAN, and have been faves during that timeframe. While I used to play Roblox back then, it was treated as nothing more but adding lag to the games that other people are playing, and online GTA for both San Andreas and V didn't exactly took off until much later.

Not listed:
Crazy Kart
Dragonica
Eligium
HighStreet5
iDate
Kian
Mercenary Online
PetVille
Skyblade
Tetris Battle
War of Weapons
ZX Online