I’m a gamer but think it’s a crap idea.
1). What games would you have? there are lots of eSports games out there, far too many to represent in a single tournament. Audiences are mostly people who play the games to (I don’t really appreciate the skill of gamers in games I know nothing about). A manufacturer of a game not selected would have a justified grievance and lose out on a lot of sales – this doesn’t really apply in other sports where they all have multiple manufacturers providing the equipment.
2). It doesn’t really fit in with the whole Olympics thing – although agree events like horse dancing has blurred this a bit
3). eSports teams are mostly commercial and it’s far more of an issue to create a temporary National team than it is with say road cycling. They’d need to practice for months to gel and that wouldn’t be possible with their commercial obligations. There’s not many solo games with a big eSports following.