Unless it's actually circular then it's going to be a very bumpy ride. If it's a circular wheel that weaves laterally it could work as described, to some extent, but the float advantages of a fat tyre would obviously be lost. Actually making a lightweight bicycle wheel with significant lateral wobble would be difficult, and the optimum number of wobbles would be interesting to work out.
Cornering would be interesting. Note that the skateboards have paired wheels so they never tilt relative to the ground, but bike wheels do. Once the wheel tilts it's no longer circular, it has bumps. So for effective cornering you would want lots of wobbles per revolution, making the rim effectively a zig-zag with a pitch of perhaps 5-10cm. But a conventional beaded tyre will not attach to that sort of rim, and the limit might be only 2 or 3 wobbles. Once you switch to a solid tyre molded onto the rim you basically have a wide rim with plastic tread on it, like an old-style tractor wheel. That will be heavy and slow, so it's probably not what they're talking about.
But a wheel with only, say, 3 wobbles per revolution will be very unstable when cornering hard. Effectively there will be three "feet" contacting the ground for each revolution of the wheel, the feet being those parts of the rim that wobble down into the turn.
- the pattern the wheel leaves when the bike is going in a straight line and upright.
- When you tilt the bike you only get one side of the pattern
- Side view, showing that only part of the wheel contacts the ground
You could make one of these using a big-wheel tubular tyre tied to a smaller, wider rim. If you used the common 622 tubular and a 406 rim like a cheap kids BMX wheel you could at least try the idea out. Kids BMX's often have enough frame clearance that you might even be able to ride the bike with that rear wheel installed.
Some of your description sounds sciency but doesn't seem to mean anything.
literally a reinvention of the wheel
This is a phrase used to market the product, and could best be considered a trademark, like "fair and balanced" or "just do it". It doesn't mean anything.
Literally speaking, a levitating vehicle would be a reinvention of the wheel, and arguably Reuleaux polygons were a reinvention at the time they were invented. If you said "figuratively a reinvention of the wheel" that would be less wrong but equally meaningless.
constantly changing velocity
That's either a tautology or translates to "bumpy". With a round wheel on a flat surface the axle has constant velocity and any other part of the wheel has constantly changing velocity. For this wheel to be different the axle would need to bump up and down (or from side to side) in that situation.
would it be more performant in certain cases
No, because it isn't human. That's a French word meaning "a man who is performing", and adjectives like "more" don't apply. Like "utilise", it's a word primarily used by advertisers, and it's reasonable to assume anyone who uses it is trying to sell you something by lying about it.