This run: https://www.speedrun.com/racextras/runs/yvnkve8m

It says it was performed on PS3 Emu. How was this achieved? Are there ways to have netplay on PC to PSN or is there something I'm missing?

Can't speak for Bellum and Adam's setup specifically but from my previous experience it's likely just done via a program like Parsec, which allows remote connection to a computer with gamepad, keyboard, and mouse support.

Local co-op for FFA in particularly is significantly faster, due to loading times and both players sharing weapon XP, so even if RPCN (PS3 emulator's netplay service) was supported for this game it would be much slower than emulating a Local setup.