Reading that I am confused: isn't hardware abstraction what the Linux kernel does? It only becomes a general purpose OS with all the distribution specific stuff.

It does, and it does a lot more than just working with hardware.

I'm sort of oversimplifying it (and probably forgetting a piece or two), but all that's needed is MMU, some minimal network subsystem with device drivers for network cards, and some very tiny VFS - just enough to handle the initrd-like thingy (the rest would be networked storage handled at the application level). E.g. if all we're going to ever run is a single VM that has its own ideas of processes and signals, we may not really need any full-fledged process scheduling or IPC, just the bits to support kernel's own threads.

A "hypervisor (or some theoretical HAL)" is literally what an OS is.