While it hasn't traditionally been seen as a sport, many professional sports players and sports bodies are starting to respect eSports as a sport that takes dedication, practice, and sportsmanship, just like any physical sport.
The next milestone for eSports is for the Olympics to accept it as a sport. The next Olympics event will happen in Paris in 2024. Paris has mentioned that they believe eSports does deserve a spot on the Olympic stage.
Their argument is that the youth are very interested in eSports as a whole, and it should be considered a sport when taking the competitive environment of eSports into account.
The difficulty with an eSports Olympic event is that in the current eSports space, competitive players and teams are very stretched between events as it is. Players and teams are often forced to pick between events and the deciding factor is usually down to prize money.
It's unlikely that the Olympic eSports event will have prize money on the line, so getting the best of the best players to attend will be difficult. Another issue is that eSports spans across dozens of different games. Deciding a single game to be showcased at the Olympics would be incredibly difficult. Alternatively, supporting too many games may be seen as a bad choice, which would give less weight to the medals earned from traditional sports.