Yes. Not exactly a standard term, but there is no standard term for what Urbit is. It's VM, personal server, yes -- but those don't clearly convey the scope of the project.

How is it a personal server if I need a personal server to run it? Am I buying compute power on other people's computers? Also, why call it an OS if it doesn't replace existing ones?

It’s a personal server OS. MS-DOS was emulated on mainframes before it was run directly on hardware. Urbit wants to do the same, starting by being emulated on traditional computer OSes, and eventually moving to bare metal.

What's a personal server OS? Will I use it to write text documents and browse the web? Can I run the X Windowing system on it? It appears to me it's currently accessed through a browser. Is that temporary?

The primary way you access any web server is through a browser.

You can access your Urbit server by command line, or by web interface.

Ah. I assumed a Server OS was an OS to run servers, not a server that exposes an OS. Thanks for the clarification!