That definition is not just loose, it's missing all of its screws completely at that point. Gambling is also assuming you're putting something of actual value at stake. Nobody would use gambling for a bit of randomness in a game with no stake.
Are you gambling with yourself in a game of solitaire? Or if you hope the Pac-Man ghost will go left instead of right at the end of the corridor? In isolation, obviously not. I'm assuming you're playing to have fun, and "losing time" or reaching a game over state earlier will not have a significant impact on anything.
However, if you'd bet $10 with someone that you'd win those games, yeah, it becomes gambling.
Aaaand that's why microtransactions blur the line so much and gacha/loot boxes should be considered gambling adjacent. Not just any incursion of randomness.
I've never played it, but I am curious about it : I wonder why SEGA never ported Jet Set Radio Future on any other platform. It never left the original xBox.
It's a bit weird because SEGA is usually not against getting a few quick bucks from the old catalogue. The first Jet Set Radio, along with a couple other Dreamcast games, has a PC version, and it's at least playable, if not absolutely perfect.