I don't know the implementation details of this specific StarTech dock, but other Thunderbolt docking stations (like the HP USB-C Dock G4) have a PCIe NIC which supports PXE booting.

It's the same implementation as an internal NIC connected over PCIe, the NIC firmware contains a PXE option ROM that the host runs during boot.

> Is it just part of UEFI?

Yes, sort of. It's the same way PC firmware has been supporting option ROMs of PCI(e) devices since the BIOS days.