Does this not depend heavily on the type of multiplayer? If there is a server running you can reject login with the error message, that they need to update.
If it is p2p you can enforce versions only connecting to the same version.
Since there is no inbuilt multiplayer support on Itch, there is also no way to enforce anything. It must happen after the user runs the app. And to do any multiplayer thing, the app needs to connect somewhere.
Maybe I am thinking too naive here, but this sounds like the type of thing, that is usually a non issue and questions like this should not even arise. If there is version incompatibility, this should be dealt with at the latest when trying to connect to the multiplayer facilities.