I like getting it straight from the horse's mouth...
Here's my disclaimer: I don't spin indoors. I ride outside, road and mountain. So, maybe for indoor cycling being able to turn the bike from side to side does make for a core workout. I don't know, because I don't spin.
On a real bike, because of momentum, there is no core fitness happening past a certain point. I'm sure of that, because I rode my bike a long time before I started exercising off of it, and my core strength didn't improve until then.
Your bike reminds me of the video games in the fancy arcades, where you can straddle a fake motorcycle and lean it side to side to play the game. Those DO engage core muscles. If you lift your feet up, you're relying on your balance to keep it from leaning all the way over to its outer limit. Similarly, a spin bike that leans like that would offer the ability to balance at the halfway point of its range of motion. That's not how a real bike works.
I think that's why I'm skeptical, and why the "real" part doesn't ring true to me. But, I haven't tried your bike, yet, so I'm making a lot of assumptions. I will report back when I do try it, though!
Karen
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insidious ungovernable cardboard