1. The primary product of an MMORPG isn’t access to a social network.
2. The social networks in these games is far smaller than social media platforms (we don’t usually worry about anti-trust for tiny markets)
3. As you mentioned, social media platforms are communications/infrastructure, not recreation.
Exactly. You can switch to another MMORPG and find another level 29 healer to restore your HP, but if your mother only uses Facebook, it's much harder to switch to a different social network and find another woman who gave birth to you.
Regardless of what program I use to communicate with my friends, that program is now a monopoly. Even if I coded up the website myself and my friends and I are the only ones to use it, that website now "owns access" to all my friends. It is absurd to label this website a monopoly.
This is also not actionable. Once my friends and I all decide on a communication platform, that platform is a monopoly and must be broken up (?), by removing some of my friends from the platform (?). In that way, it would literally be impossible for me to have a platform where I can communicate with all my friends, because such a platform would be a monopoly and must be broken up by your definition.
2. It's perfectly actionable: open protocols separate the platform and the network.
For example, my colleagues are on Twitter but not Mastodon. I can't leave Twitter without leaving my social network. Why does Twitter own access to my colleagues? Why should we allow that to be a competitive advantage? It's certainly at-odds with the principle of innovation--you're not on a platform because it's more innovative than another platform, you're on it because they have a monopoly on your social network.
Contrary to your claim, there's very little competition in these markets because corporate ownership of user social networks is an enormous moat. Not only can users not easily move to another platform, but advertisers can't easily spend their money on some new platform because the new platform is much smaller in all likelihood.