Yeah, pretty much. Modern console emulators tend to use an emulation technique known as HLE (high-level emulation). This involves translating a system call made by the emulated system and replacing it with a similar native function call on the host system.
Basically, you'll have a recompiler pass through the code of the emulated system's executable, and whenever a syscall instruction is run into, it'll be replaced by the equivalent function in the output (recompiled code), which is then run natively on the host system. Since the XBox and PC both use x86 CPUs, it's more along the lines of Wine/a compatibility layer than emulation (at least on the CPU side), since code doesn't have to be translated from one ISA to another, only syscalls are dealt with.
Windows and XBox syscalls are very similar (and in many cases the same) so that makes translating XBox syscalls to their Windows equivalent more convenient.
The problem with using a hypervisor/virtualization is, like you said, the other components of the system that need to be emulated. I don't know if you can setup virtualization to work like that, I think you are only provided with general virtual hardware, or access to your system's hardware (I really don't know though, haven't dealt with virtualization much).
Anyways, if you're looking to get started in emulation, take a look at the CHIP8 thread. CHIP8 is the hello world of the emulation programming scene, it'll introduce you to the basic structure of an emulator, and shouldn't take long to get working (probably a couple days). The next logical step after that would be the GameBoy, SMS or NES. They'll get you introduced to the other main aspects of emulation and what systems are really like on a low level, ex. interrupts, MMIO, "realistic" video and audio systems, etc.
After that, well, you'll have to decide. Some people gradually step up the system complexity (SMS -> Genesis/Mega Drive, etc), others jump right to the more complex systems. Most of the techniques involved with emulating more modern systems can really only be learned by actually emulating or studying them, like the specifics of the graphics and audio hardware, since they're much different than the ones in older systems.
Hopefully I didn't make that too confusing, lol. If I have, just point out what you want to know more about, I'll try to help. I don't know exactly how much you know about emulation and systems on a lower level, but you seem to have the general idea.