No part of a Unity game runs in a .NET VM or any other VM. They chose C# as the scripting language because C# is one of the most popular programming languages, it's extremely popular in the non-game dev development community, and it's probably the only non-Web language that most code academies teach for traditional development maybe other than Java.

It's syntax is also pretty close to C and C++ which means developers with game dev background will feel at home as most game development is done in C++.

Unreal Engine uses Unreal Script which is now pretty much C++ but it is also not compiled directly (although with Unreal Engine 4 and onwards it's much closer to direct compile than any other scripting language).

Unity engine has it's own interpreter which then builds highly optimized C++ code and compiles it when you build the game.

Unity Engine is a pretty decent engine with kickass performance when optimized, without fine optimization any general purpose engine including Unreal 4 acts like utter crap. I'm alpha/beta testing a few UE4 games atm and you can see just how bad performance can get even on a solid defacto industry standard like UE4 like when dynamic shadows tank a GTX Titan X (Maxwell) SLI setup to below 20 fps any time there are light sources that are not properly fenced and culled - e.g. explosions.