What does this error even mean and why is this relevant to speedrun.com?

Probably to ensure that you're not a bot/it's your account, Something like that, Not really sure about it, But overall staff knows more about it than us.

Also why are you literally asking here lol, I don't think anybody else figured out that.

It's because as a moderator there needs to be at least two ways to contact you off-site. When you request a game, you are requesting to become a moderator for that new game as well, so you need to meet their requirements for being a moderator.