"...Batman is the personality-shelf where Bruce Wayne stores the crazy-plates..." - is this just a metaphor, or is it something else?

It's an analogy using coinages formed from similes:

To be a plainer metaphor it would not have been as you suggested, but rather:

…Batman is the shelf where Bruce Wayne stores his plates…

The problem being, that it's too far from the intended purpose for anyone to get the metaphor. A simile that states the comparison more directly would be:

…Bruce Wayne stores his crazy in Batman much as one would store plates on a shelf…

Which is just ridiculously weak, and shows just how stupid the analogy is.

Instead they create a concept of crazy-plates and a concept of personality-shelf as if there was some sort of natural analogy between them, and uses them accordingly. These newly coined concepts originate in a simile, but once coined their use is then plain: If crazy-plates and personality-shelves made any real sense, then the use of them would not be similes, though they themselves would be similes (similes rather than metaphors as they state their comparison explicitly)

Comparably, I'm not using any metaphors in structuring the sentence "I rebooted the firewall", though I am using a metaphor in each of reboot and firewall, most server rooms having neither bootstraps nor steam engines.

This case stands out more than "rebooting a firewall" partly because its fresher (boot[strap] and firewall are dead metaphors that have become new general senses of those words) and partly because it's an extremely bad simile, though that is a success in itself as it derives its humour from being deliberately bad.