Not charging you for something is a pretty conventional definition for "free." Of course, they have their own motives to not charge you for hosting videos--which includes making money off associated advertising.
"I'll allow you to give me a lunch, for free." might be true (if I wouldn't charge you money to allow you to give me a lunch), but it seems like an odd statement to make.
Of course, this is not a super close analogy, because you wouldn't be gaining anything by giving me a lunch.
I think a closer analogy might be barter, maybe? Or, here is an odd analogy that might fit fairly well, but which maybe goes against the point I was trying to make:
If one person wants to interact with a pet dog, because they like dogs, and another person wants their pet dog to be taken care of for a while, so the first person agrees to take care of the other person's dog for a while. This case does seem to capture a fair bit of what is happening, but it seems like it makes sense to call it "for free".
Here is a variation on that idea though, which seems a little closer, but a bit less clear cut:
What if the person who is taking care of the dog for a while also said that they were going to enter the dog in a dog show (and that maybe if they got prize money they might share it with the dog owner), and that the owner of the dog was pleased by this idea. This would be a quite strange situation, so maybe intuition based on this example might not be the best guide to other things, but my intuition in this case is that it seems like it seems a bit more strange to say that they are doing this for free, though it would still be technically true.
(The dog show is analogous to showing the video(the dog) to other people, and the prize money is analogous to ad revenue, in case that wasn't clear.)
