True but games also added client side hit prediction which the Quake engine games never did. As late as Quake 3 if you were using a railgun you would have to lead your shots. There was the ZeroPing mod for UT then Valve put client side hit prediction in Counter-Strike.

Was some controversy as people said it makes it easier to write cheats, I remember even Cliffy B from Epic Games wrote this blog post about how terrible it is but that is where games went and IMO its a lot better then 1990s netcode.