Yes, I *still* have to look this up sometimes because I've used and made so many engines and tools that I don't know which hand is which and which way is up half the time ;) Gotta laugh at UE in the corner on its own there.
Ogre was right-handed (aka the canonical way if like me you learned from the Red Book) but had no concept of "up", technically. It could be whatever you wanted 🤷♂️