Man page says that project is a GTK2 project.
I posted a bug report to Ubuntu, asking about a documentation bug regarding the mutter(1) man page on my system, and elsewhere on the internet, that claimed that the project was using GTK2, when the project probably isn't using GTK2 on my machine.
I don't know for a fact that my Ubuntu system isn't running mutter using GTK2, but I suspect that it's probably a documentation bug, since Ubuntu tries to use later versions of GTK in their projects. Also, GTK2 apparently hasn't been the default version of GTK used in mutter since 2010, going by this commit in your repository: