Fix game path not properly updating (LiveSplit#37)

This fixes the issue where you would change the game path but it wouldn't actually update it so clicking start game would open the file from the previous game path.

src/lib.rs

@@ -1052,6 +1052,7 @@ unsafe extern "C" fn update(data: *mut c_void, settings: *mut obs_data_t) {
 
     handle_splits_path_change(state, settings.splits_path);
 
+    state.game_path = settings.game_path;
     state.auto_save = settings.auto_save;
     state.layout = settings.layout;