The short answer is that a defense of dualism is not what John Searle was doing with the thought problem. He was showing how knowledge is different from function -- IE it was an attack on functionalism.
Longer answer: Searle would agree with your further elaboration on the paper version of an algorithm being no different from an electronic one, and neither being plausibly identical with consciousness.
Searle's argument is a thought problem, designed to exercise our intuitions, not an experiment. It is therefor not definitive -- it is possible in principle that SOME kinds of algorithms could be identical to consciousness, and that perhaps the "running" of an algorithm (Searle would note that "running" is not a logical state, so this is an invention of some new criteria, not actually functionalism) matters, and maybe it is the method of running, not just the algorithm that gives rise to consciousness.
Searle’s thought problem however has had a significant impact on philosophy of mind. IIT is explicitly postulating the response above -- Algorithm PLUS running it on a substrate with a large Phi is needed to create consciousness, per IIT.
Searle was a biological emergentist, so he was a form of physicalist. His response to your casting the Chinese room as an argument for dualism, is he would have argued that we have good reason to think the mind is dependent on the brain, so he speculated that there was some aspect of the biology of brains that cause minds to emerge from them. Most physicalists today have followed Searle and are not functionalists, but instead are emergentists, like Searle was.