While I do think that 9-year old kids shouldn't be playing online multiplayer games at all, your reasoning about EULAs and contracts is dubious and brings common misconceptions. While they're rarely challenged in courts (mostly because most people can't afford it), there's been lots of debate and arguments against the legal validity of such contracts.
I suggest you read the book "The Software Conspiracy" by Mark Minasi. While the main theme of the book is advocating for less buggy software, one of the chapters is called "Software and The Law", and it includes a very in-depth look at TOS'es and EULAs and reasoning why pretty much all of them are illegal. While the book centers on shrink-wrapped commercial software and some of the arguments might not apply much to "free" online services (which are not really free - if you don't pay a fee or subscription, that means you are the product), many still hold true, especially the argument about these sorts of contracts being cohercive and non-negotiable.