VideoCommon: Header cleanup

Also remedies places where the video backends and core rely on things
being indirectly included.

Source/Core/VideoBackends/Software/TextureEncoder.cpp

@@ -2,6 +2,10 @@
 // Licensed under GPLv2+
 // Refer to the license.txt file included.
 
+#include "Common/CommonFuncs.h"
+#include "Common/CommonTypes.h"
+#include "Common/MsgHandler.h"
+
 #include "VideoBackends/Software/EfbInterface.h"
 #include "VideoBackends/Software/TextureEncoder.h"