For me it was Quake II on the Nintendo 64. Didn't even have a LAN, just a big-ass TV split into quads. It was a skill to watch your own screen but also everybody else's so you knew where they were in the arena. My buddies always went for the BFG which was effective of course but pretty crude. I secretly spent months playing the single-player campaign and practicing like crazy with the rail gun, which could also take people out with one shot but was very difficult to get a hit with. I got so accurate with it that my buddies accused me of cheating somehow -- the ultimate compliment.

And this was around 2003 - 2004, almost a decade after the N64's heyday. You just don't need the latest shit to have fun. Give me a stick and a hoop and I'll be happy.