If this is what's happening and you do find a way to block the game, you're missing the point. Which would quite possibly be, as above, addiction.
There are plenty of other games - or alternatives to games - to get addicted to. Blocking access to one doesn't fix that.
And if he figures out what's going on - i.e. that the IP addresses are blocked and that someone
must have blocked them - your credibility with him will be utterly shot.
Which he might figure out e.g. by contacting the game support staff or using an online forum, like you are doing. If you can figure out how to do it, he'll be able to figure out how it was done.
This doesn't seem like a plan that will end well.
Also in terms of providing technical advice here, we should be careful as we don't know what the situation is. We're only presented with one side of it. This will sound harsh, but it's not directed at @wesc
at all, rather at internet forum discussion in general. It's a common difficulty with giving advice that could be used against someone else - a bit like when someone says they've 'forgotten their password on a laptop, is there any way they can scan their laptop to get it back?' they're basically asking for advice on how to hack someone's password. Except here it's advice that is explicitly to be used to interfere with someone else's use of a computer.
I hope you all can work things out with your brother - it sounds like he is lucky to have a caring and observant family