Technically I guess Spacewar! was the one who started e-sports, was the first game people competed in. Personally, growing up in Sweden, I think FPS (namely CS1.5/1.6) was the first game that enabled people to play games professionally on a international level, so I'll always associate CS with starting that, but again, technically I guess Quake was the first FPS people competed in professionally, at least in the US.