Firstly, if C is for "computer," then every single RPG that we're talking about is a CRPG, in which case what's the point of adding in that extra letter?
Because role-playing games were being made and consumed by people who played D&D and probably people who made a few ttrpg systems of their own, adapting them for computer games. I bet people didn't start saying 'tt'rpg until cRPGs had become the dominant driver in the culture.
