A much better analogy would be watching other people play board games.
In certain circles, chess and poker have become spectator sports.
Also, we're talking "let's plays" here. There's no "skilled play" involved. It's an idiot with a camera playing a game poorly while making dumb jokes. It's dumb, it's pointless, and it's copyright infringement. Just ask Nintendo.
This is why e-sports won't take off, as the publisher has power to shut down any league competing with the publisher's approved league.