It's not though? If we were actually storing the parameters describing the state we'd need 8x10^300 bytes = 8x10^288 Pb (assuming each "continuous parameter" is stored as a double precision float).
I do think the author exaggerates the difficulty though. The impossibility of even storing a complicated quantum state on a classical computer just shows how different the world is from a classical computer. The world is quantum. The state space of the world cannot be stored on or manipulated by a classical computer.
However, the authors point does show that if we build a quantum computer you will not be able to place it in every possible state (like you can with a block of memory in a classical computer). The space of states in a qc is just too large. That's very different from computer systems we're used to.
Edit: I found this interesting: https://www.hpcwire.com/2019/01/09/the-case-against-the-case...