Now my question for the casinos which label demo mode playing as 'fun' is, does it mean that those who place bets with real money are not having fun and are just after chasing for a chance to increase their staked money, or what?
Maybe that's not the reason behind their naming, it's not the way you are thinking, fun is the simplest word that's too easy for understanding it.
Demo is meant to learn how the game works while giving you that gambling experience and entertainment, but referring to it as 'fun play alone' makes real bettors, to me, fall under the category of desperate gamblers.
Depends on the bettors that interpret the way he understands it, I don't see it that way, but an expression to the public to what they mean.