Add missing includes where headers depend on other headers having been included first.

This is good hygiene, and also happens to be required to build Dolphin
using Clang modules.

(Under this setup, each header file becomes a module, and each #include
is automatically translated to a module import.  Recursive includes
still leak through (by default), but modules are compiled independently,
and can't depend on defines or types having previously been set up.  The
main reason to retrofit it onto Dolphin is compilation performance - no
more textual includes whatsoever, rather than putting a few blessed
common headers into a PCH.  Unfortunately, I found multiple Clang bugs
while trying to build Dolphin this way, so it's not ready yet, but I can
start with this prerequisite.)