Fork aside, a bike wheel's structure is based on supporting the load on the hub by hanging from the spokes at the top of the wheel. In order for that machine's wheels to not fold in half the rim would have to be incredibly heavy and slow.

Now that you mention it... This doesn't look like it would actually work once a human being is actually on it. All the weight is gonna be on the tires and the part holding (and presumably spinning) the tires. Also: What the hell are the pedals connected to?

Never mind how strong the thing itself is, that joint is basically impossible to engineer so that the wheel can't rotate side to side. That is, rotate on an axis it's not supposed to. Sure, you can prevent an (essentially) round thing from rotating with a pipe clamp, but now try to do that while allowing freedom lengthwise.

That wheels are round and not pipes help a bit, there's some lever purchase you get from the radius but in general, nope. You're still sitting at the short end of the lever.

Diamond frames with spoked wheels are literally the optimal solution to the problem the rest is compromise (e.g. having no top bar for comfort) or overengineering.