It’s just a name. Whatever they call it, as long as you’re playing without risking your own money, that’s automatically demo play. No need to complicate it. The effect it has on you is your own thing, but the obvious purpose of demo play is to let you learn the game and get an idea of how it works before you start risking real money.
It seems there are so many linguists in this forum, even the words that people already understand from the first time they read, but @OP make it complicated.
@OP I suggest you to send a message to the casino for changing the words fun play to practice/demo/not gambling etc.
Its just a matter of choice of words. It could be fun play, demo, fake play, free play, etc.
Don't say the bold words, @OP will questioning whether the game is fake/different/manipulated compared to "real play".