The multiplayer games I played most on pc as a kid were Golden Axe, Firepower and Ironman offroad racing.
This had vertical splitscreen multiplayer. You could lay mines to defend your base and then try to sneak into your friends base to capture the flag. Being able to see your friends screen made the game a lot more fun. The large maps would not work with online multiplayer.
So many hours lost on this while we should be doing homework, the later tracks get pretty tricky.
We hardly ever made it to the end, one accidental hit on eachother always result into a full on deathmatch, good times.
Lemmings was for family time. The sheet with level pass codes was always right next to the pc, taking turns and suggesting different solutions. And later worms was cause for fierce competition.