They almost certainly are running at a loss. Same as Twitch, their parent companies are generally okay with it, because they also serve as pretty solid tech demos for other services they offer (YouTube runs on Google Cloud Platform, Twitch runs on Amazon Web Services), and that pays off indirectly.

Moreover, their parent companies can use them as free advertising. Google about to launch a new phone? Guess what you’re gonna see ads for!

I think the term for this is “loss leader”