core/dumping: Add FFmpeg implementation

Sorry for the large diff, the implementation is quite long, and I can't really find a good way to split it into commits.

src/core/core.cpp

@@ -17,6 +17,9 @@
 #include "core/core.h"
 #include "core/core_timing.h"
 #include "core/dumping/backend.h"
+#ifdef ENABLE_FFMPEG
+#include "core/dumping/ffmpeg_backend.h"
+#endif
 #include "core/gdbstub/gdbstub.h"
 #include "core/hle/kernel/client_port.h"
 #include "core/hle/kernel/kernel.h"
@@ -218,6 +221,12 @@ System::ResultStatus System::Init(Frontend::EmuWindow& emu_window, u32 system_mo
         return result;
     }
 
+#ifdef ENABLE_FFMPEG
+    video_dumper = std::make_unique<VideoDumper::FFmpegBackend>();
+#else
+    video_dumper = std::make_unique<VideoDumper::NullBackend>();
+#endif
+
     LOG_DEBUG(Core, "Initialized OK");
 
     // Reset counters and set time origin to current frame