eSports are eSports. They have a different name than "sports" because it's not the same thing. It has a similar name to "sports", because it's a similar thing.
Regarding cheating: Yes, because real sports, especially the professional/competitive level, is known to be free of cheaters.
Arguably, eSports cheaters are much easier to catch because by definition, everything is controlled by a computer and most cheaters leave some sort of trace that can be tracked. I'm pretty sure that you will find no physical sport that has as strict an enforcement of anti-cheating rules as even the most lenient/lazy competitive eSports games. Especially at the highest level of play, during tournaments where competitors are physically present, with hardware provided by and players under observation of judges, cheating is practically impossible. Many physical sports would be better off if their tournaments had the same ratio of cheating as eSports.