Whether esports count as sports has been asked by many people, in good and bad faith, many times over the year. Your personal answer to this question likely depends on a lot of variables; where you grew up, what you did in high school, etc.
The technical definition of a sport is “an activity involving physical exertion and skill in which an individual or team competes against another or others for entertainment.”
By this definition, esports are absolutely sports. The level of physical exertion one would need to play an esport isn’t the same as, say, American football or basketball, but there’s physical exertion. There’s also the element of competition for entertainment; esports fill arenas world-wide. If filling arenas and needing extreme amounts of hand-eye coordination doesn’t define these games as sports, well what does?
There are those who would say the level of physical exertion is too far removed from competitions that are normally labeled as “sports.” In the same way we don’t view bowling or darts on the same level as tennis, we don’t view esports the same way we view other, more physically stringent sports. Other than a few, isolated cases, playing League of Legends doesn’t make the player pour sweat the way tennis does. This argument is predicated on esports being so far removed they really don’t fit in the same category.
This doesn’t exclude esports from the sport category, however. Without a hard and fast definition, it’s difficult to say definitively