This means that the upper bound of computability is "10^{120} ops on 10^{90} bits." Question: does this upper bound apply to quantum computers as well?

It does, assuming these are reasonable bounds. The author is using atomic spin as the most elementary bit and a spin flip as the most elementary operation (a bit flip), both of which are used in quantum computers.
It can cause some confusion the fact that a quantum computer makes use of quantum superposition, since then a single operation in n qubits yields twice the information processing as a single operation in n-1 qubits.
Nevertheless, a single operation in n bits consists of n elementary operations (bit flips), and this is what the author is counting. We're counting the number of elementary operations, independently of whether they're performed in parallel or are part of the same physical system.