Okay, in Random Bundle Game, select "Download" in the little panel for each game. Or in itch.io/my-purchases/bundles, select "Download" in the long list. This won't immediately download each game, just add it to my library.
I don't want to rely on the itch app because of the seizure risk.
I still need to figure out a good way to organize these, list which ones I can or can't use, might want to try, etc.