1) Cutting down costs by moving some streaming traffic to Youtube servers.
2) Free advertising. There are millions of Youtube users. If few of them take note of a Youtube user "GOG.com", and actually visit the site, it alone makes it a good choice.
3) Standard video format. Now in some cases Youtube may be blocked, yes. But on the other hand, if Youtube is working for other purposes, then it's also working for GOG videos. Hosting videos otherwise might in some cases make them available where Youtube is blocked, but in some cases cause videos not to play for some users.
4) Hypothetically GOG could use Youtube as a channel for certain "push" kind of messages, for instance they could create videos to promote sales and such, and people who subscribe to their Youtube channel could get notifications of those. Now I don't think GOG does that (then again I don't know, as I don't subscribe them), but at least that is an option they have.