It depends where you are in the world. I believe they're exceptionally popular in some parts of Asia like China and Korea. In places where everyone has a personal computer powerful enough for everything they do with it, and with a tablet/laptop just about every cafe is an internet cafe.
Even still, there are niches to fill in such places. Relatively recently (last year I think) a place here opened with exceptionally high performance PCs/net connection, comfortable chairs, etc, which focuses on gaming. Every time I walk past it's packed, so they're doing something right.
Do those still exist? I remember playing StarCraft a lot with friends in such a place, but this was like... 8 years ago?