I'm suggesting that there's an option on your hotbar, in every minigame, to invite a friend. The main reason I believe this is necessary, is that it's sometimes hard to get enough players into some of the games in order to start. The item would be a simple head, with the title "Invite a friend" Upon clicking it, your list of /friends will pull up You'll click on the friend you wish to invite, and a message similar to this will be sent to them I'm unsure how the "ACCEPT/DENY" system would work. Maybe a command to accept/deny? Most of the minigames have a hotbar fairly similar to this (excluding bedwars & bvz) So, you could just add an "invite a friend" option on all of them.
Support. I think the accept and deny command should be something like /g accept /g deny (Game deny or accept)
I can see this being an issue if it were inviting anyone. But, you can only invite someone who you have on /friends, meaning you can always unfriend them if they are annoying you with invites.
Support, seems like a great thing to implement the server, maybe a sort of inbox added with it that shows your invites and doesn't just spam it in your face :P maybe /invite inbox and it would pop up to a page similar to your design with everyone's invites.