Sure, there are companies that provide entertainment or fulfill desires. But even in those cases they offer something that's missing, something that one is seeking. Those might not be serious problems with pain points you need to deal with immediately, but problems nonetheless.
I guess you could argue what a problem is. To me, a problem is when I have a need that's not satisfied.
Yeah it's easy to play word games to describe everything as solution to a problem but that's really just cheating to be able to actually say "every business is the solution to a problem".
For example, "entertainment/games are the solution to boredom". You'd only say that if you really wanted to back the idea that every business must be the solution to a problem.
Hard to argue that Twitter solves a problem, nevertheless there's an awful lot of people using it constantly. In the "every business must solve a problem" world, you could say "Twitter solves the problem of people needing to communicate with all the other people in the world in public conversations", but that's really trying to force it.
I also agree that trying to force "problem" into the discussion isn't useful, and in fact is counter-productive because you're verbally moving further away from what the business is really doing.
So perhaps the whole thing should be qualified as: In the case that a business is solving a problem, which _is_ typically the case in B2B (notice all your examples were B2C), _then_ this is a useful way of breaking down the typical questions you should be posing yourself.
That statement is a much more generalized statement about what the basis of a business must be, whether or not it solves a problem, for a business to succeed it must provide something that people want.
In writing this comment I suppose it could even go further and say "make something people want or need". For example insurance and legal compliance are not things people tend to want, but do need.
That makes sense. I agree, it's more universal and elegant than just solving a problem.
See: Yelp