The internet was not widely popular before Quake, though. It was just starting out. You had stuff like CompuServe, AOL and Usenet. So you were "on Compuserve" more than "on the internet". At that time, people were still playing Midimaze on Ataris (which used the MIDI connector for networking!). Doom and Quake over the internet were pretty new things. A "network" was usually meaning a LAN, company or home. I remember us using a nullmodem cable to connect two PCs to play Doom2, probably in 1995.
Anyone remember these?
Internet means inter-network, with network meaning what I said above. Net-Quake was run on a company or campus network. Quake"world" probably stems from "world wide web" which was another popular 90s term. The whole prediction stuff was done because most people used this:
Since the internet is a lot faster today, and will probably get even faster in the future, Netquake is an option for the internet, and the faster the internet gets, the less use there is for prediction.