Uhmm, I was not sure wether to post or not, because it seems that many people in here are a tiny little ignorant. But well, what can you lose.
Of course it have the right to close a streamer who promotes a private server running their own game. What in the world makes some people think that they somehow own this game? It's not just because they lose money from the loss of players migrating to this server (and yes, of course the lose money. Probably nothing compared to the big picture, but still).
Don't get me wrong, I still love to play vanilla wow here, but if Blizzard went after streamers and the server itself (witch I am sure won't happen), then I'l be fine with it. It's still their game even though some french people have decided to broadcast it for free to the world without having contributed to the making of the game itself.
Make a new stream. But grow up and don't be mad if it gets shut down.