Conveniently, I'm an engineer who works with TPU all the time.
(Very different application, though--unfortunately!) Like PVC, it's not a single thing, and comes in many formats. Some of those are soft, conformal sheet materials, almost indistinguishable from the PVC/Vinyl sheet materials commonly used to make plastic pants. Put another way: If you've used other plastic pants, TPU pants
probably don't have many surprises in store for you. TPU is often described as being a more durable material, but there are so many factors involved in the durability of a final product that I wouldn't assume TPU pants are necessarily better.
I doubt it, although there are TPU-coated nylon materials out there. I suspect these pants are like the common PVC/Vinyl ones in terms of look and feel. That said, TPU-coated materials are commonly used for diaper covers. When the TPU is laminated onto polyester fabric, you get PUL (PolyUrethane Laminate), a super common material in the world of cloth baby diapers. If they were talking about PUL, though, I expect they'd have said "PUL" and not "TPU."
Try 'em and give us a review!
EDIT: Didn't notice you'd put the website in your post. I looked. Seems like they have a few varieties, including some water-clear pants that look extremely wrinkly, though I expect these still have a very soft feel and don't crinkle. (Probably they were wadded up really badly when packed.) Some of the other products talk about "TPU backed" cloth diapers, although it's a little unclear what that means. They do also mention PUL, so I guess "TPU backed" is just a solid-color TPU sheet sewn over the diaper.