In the context we're arguing fun means "a childish measure of how people enjoy a past-time." Hence why I put fun in quotes.
Except, it doesn't when it applies to games. No matter who it comes from, subconsciously their enjoyment derives from the other definition of fun. The only thing is that people don't study what fun actually is, so they have a bunch of preconceptions as a definition instead. That doesn't change the fact they are still, inside their head, voting based on what they learned.
That's the whole reason we enjoy different types of games. Each of us takes different lessons from different things. Some people can learn from the story (story is the most powerful way to teach a lesson since it causes a whole bunch of memory receptors to fire off and allows the brain to make all kinds of interesting connections, btw), others require deep gameplay, and some people are comfortable with some types of gameplay (like fast-paced shooters and platformers) and others can only enjoy other gameplay (like RTS and MMOs), all because of the boredom mechanism.