To illustrate - imagine you give the room (in Chinese) the text of Lord of the Rings, and then ask it which member of the fellowship corresponds to the "Wise Old Man" archetype. Any reasonably smart human will give the answer, "Gandalf". But the room would need to (in Chinese) make systematic notes of the characters, their relationships, their actions, and then somehow integrate all this into a categorisation under the appropriate archetype.
I'm actually agnostic as to the question of whether such a room could be built -- as I'm agnostic towards the possibility of AI -- but assuming the room would not be inconceivably complex masks the complexity of the ordinary workings of human consciousness.
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Essentially: consciousness does not exist. We only think it does because the thing we think with is wrong. But because we think with it, we can't tell the difference. So asking "who is experiencing the illusion" is begging the question.
As for your essential point, I hold that words like "think", "experience", "illusion" all rest on the more fundamental concept of "consciousness".