The poor floating point performance of many PCs at the time meant that a lot of code used ints rather than floats, making determinism much easier for multiplayer!

I believe DOOM and Warcraft 2 simply did lockstep determinism across all clients. You could run the simulations forward completely deterministically due to use of its and fixed point math.

Quake did as well all the way up to Quake 3 I believe. The game was basically on a heartbeat based on the worst latency of the connected player. Everything got synchronized that way.

Back in the day, your gaming could be super wrecked if someone with a 300ms latency joined :D.