How was this rattan chair constructed?

According to the B&B Italia website, it is a powder-coated aluminum frame wrapped/woven with “polyethylene rope”. I don’t see a rattan version (?) but this is what is commonly referred to as “synthetic wicker.”

You could do the same thing with real rattan/wicker, but it would require the same metal frame. Rattan is not terribly rigid on its own, which is why you rarely see it used as single-pole structural component in diameters less than ~1.25", and even that’s a bit flimsy for something like this.