I think that if local connections are separated from the "existence of the Internet", then it is quite possible. E-sports would still develop within the stadiums, there would also be areas for competitions and training. It is logical that the process would have slowed down, although without the existence of the Internet, other types of competitions (classic sports) would also develop much more slowly.
Suppose more efforts would be required to hone the players' skills, only a few became real champions, due to the inability to participate to everyone who wishes in the game battles, as well as the existence of a real selection of participants in teams to perform at world arenas. This would require large financial costs, accurate analytical systems, more organization on the part of both the tournament participants and those who hold the competition. I think people's attitude towards esports would become even much more serious, which would raise it to the podium in sports competitions. After all, the only thing that hinders him (sort of) is that games are available to everyone, and the older generation often has "toys for children", and they consider purchased circus performances with a bunch of lies for the sake of advertising a sport (well, there are Olympic games, world championships on football).
If you're talking about competitions in Dota 2, Cs and others, then I think not. Since these are team games. Could five (conditionally) people sit at someone's house or in the garage and go through the levels (and what else is in offline games). And then one day they will get a call or write in the newspaper about the competition. They will go, but what's the point they don't know other strategies, the choice of characters, chips.