[rdw]

It has more to do with how game engines are built, making embeddability be the most important criteria.

Most game engines are written as a large chunk of C++ code that runs each frame's timing, and the big subsystems like physics, particles, sound, and the scenegraph. All the important engineers will be dedicated to working on this engine and it behaves like a framework. The "game logic" is generally considered to be a minority of the code, and because less-technical people generally author it, it gets written in a higher-level "scripting" language.

This creates some serious constraints on that language. It must be possible to call into the scripts from the main engine and the overhead must be low. The scripts often have to make calls into the data structures of the main engine (e.g. for physics queries) and the overhead of that should be low as well. It should also be possible to control the scripting language's GC because the main engine is pretty timing-sensitive. Memory consumption is pretty important as well.

All these requirements point towards two implementations specifically: Lua (and LuaJIT), and Mono. Those two runtimes go out of their way to make it easy and fast to embed. A third option which a lot of engines pick is to write their own scripting language where they control everything about it. Any other language you can think of (with the possible exceptions of Haxe) will have some major hurdle that prevents easy embedding. The fact that you can compile multiple languages to Mono bytecode pushes some folks in that direction; if you're planning to write a lot of code in the scripting engine (not all of them do! See: Unreal) that's nice flexibility to have.