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“It did things a person wouldn’t guess, such as changing one laser’s power up and down, and compensating with another,”

This sounds suspiciously like slapping the term "AI" on to a oscillating feedback control loop.

I'm sure a Gaussian process could model the equivalent of feedback control; they're pretty flexible (if not as flexible as NNs). The trick is coming up with something that can learn the feedback controls, or lack thereof, on its own. Unsurprisingly, they're reinventing reinforcement learning.
"Artificial intelligence is what we can do that computers can't ... yet"

You're not far from wrong, but look at the original article.

Source code here: https://github.com/michaelhush/M-LOOP

This is a neat application of ML! In the same way that automated theorem provers have had huge impact on doing mechanized proofs, perhaps "automated lab assistant" could have a similar impact on the experimental sciences.

It looks like they've hooked up standard function optimization techniques to their lab equipment. Nothing new from an ML perspective. Is there something clever in the way they parameterized the space of possible experiments?
No, this is standard issue ML. It's the application that is neat, not the technique.
Pretty good sense of humor from that author:

'This AI is extremely specific in its design, of course, ... for more flexible automation, physicists will still have to rely on the general-purpose research units called “graduate students.”'