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I would assume that they're talking about redshift.

Yes, but one half of a galaxy would get redshifted, and the other blueshifted, no matter which direction it spins in. So why would that change its overall brightness?

(Though one of the papers notes that the tiny change in brightness this causes isn't enough to explain the large difference in spin directions)

The close and far sides get shifted too, and those have different brightness.

No, 'like_any_other has it right: any physical system is 1-to-1 isomorphic with its mirror image, which is spinning the opposite direction.

Whatever asymmetry you're visualizing for one galaxy, its mirror-image galaxy is equally physical, and possesses the same asymmetry.

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