Comparing consciousness to how a CPU processes instructions is very poor analogy, because to this day, because the nature of consciousness is still a complete mystery to science.

I mean, we can think about stuff, but we don't think about them one after the other. We're thinking all of the time, but we tend to focus on what's immediately interesting to us. Consciousness is a pretty complex thing to unravel...

I think it’s likelier that each portion of the brain fires away at up to whatever its natural “throughput” is (some activities more or less parallel), and conscious awareness just happens to feel like a single global mutex.

I guess this is a game you can play where you keep refining the analogy until it’s too complex to help, but I don’t think the linked author’s analogy is good or useful. Better to just say we can’t be consciously aware of two things concurrently. It’s not a hard concept.