In the last paragraph, there is

public void onSaveInstanceState(Bundle var1) {
    super.onSaveInstanceState(var1);
    Bundle var2 = this.c != null ? this.c.e() : this.b;
    ...
}

so you can do

@Override
public void onSaveInstanceState(Bundle outState) {
    super.onSaveInstanceState(outState);
    final Bundle playerState = YouTubePlayerViewUtils.getPlayerState(mYouTubePlayerView);
    if (playerState != null) {
        state.putBundle(KEY_PLAYER_VIEW_STATE, playerState);
    }
}

And modify the creation

@Override
public void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    mPlayerState = savedInstanceState != null ? savedInstanceState.getBundle(KEY_PLAYER_VIEW_STATE) : null;
}
@Override
public View onCreateView(LayoutInflater inflater, ViewGroup container, Bundle savedInstanceState) {
    mYouTubePlayerView = YouTubePlayerViewUtils.createYouTubePlayerView(getActivity(), mOnYoutubePlayerInitListener, mPlayerState);
}