I'm by no means an expert at japanese either, and all of my knowledge comes from merely watching too much anime, but onee and onii can also be used as terms of respect toward any older female or male. Not sure if that's the case in the video though, as I haven't seen it just yet.

EDIT: Having seen it, I think your explanation was right, and they're talking about Lightning. Also, it was very entertaining to watch that video and actually understand some of the words even without subtitles though, and even more entertaining how even the parts that I didn't understand seemed totally natural and familiar.