Unless the people who own the rights to a game give explicit permission, you're not allowed to monetize gameplay videos on youtube or livestreaming sites since it's specifically against their ToS. For things like Minecraft, the creator made a blanket statement basically saying anyone can monetize their gameplay footage of Minecraft.
This is why youtube partners typically join a network, like The Gamestation, since the network acquires these rights for them and handles the legal stuff (from what I understand). In return, they get a portion of the ad revenue.
Source: TotalBiscuit's Twtter
EDIT: So yeah, it would be a good idea to get permission from Alex, or even a blanket statement from Alex allowing the monetization of gameplay footage (it would be decent advertising, what with MS suddenly choosing to forbid this sort of thing for their games). And if you tweet to let TB know, there's a decent chance he'll retweet if you identify yourself as the developer.