A "bare metal" display server can run in VMs, or even in containers (although the latter is a little pointless as the device access violates sandbox safety).
I'll have to say though, I find that particular definition of bare metal quite strange.
"Nested" is more or less the de-facto term in Wayland-land for the child scenario (pretty much all Wayland display servers natively support a rootful child mode either as real feature or for testing/debugging, some even under X), but there isn't really a good word for the normal case.
It's true that you don't have to, but you certainly can.
In fact, the first implementation of containers in Linux - Linux Containers, or LXC - works exactly that way.
This may or may not be as great a distinction as you might want in order to consider it bare metal vs. not. I'll leave that up to you.
Operating systems can run on VMs or containers. When comething runs on top of those OSs, they are not running on bare metal.