It seems plausible that social networks have more of a network effect than things like a game streaming platform. Obviously there's still some network effect and a certain marketing aspect to it, but I don't think they're directly comparable.
You have to convince game developers to port their games. If the reward is a few thousand users, it's going to be a hard sell. Also the R&D and infrastructure required to even start up the project is too high. Building a Gmail (especially back then) is small potatoes in comparison.
