This is a classic example of feature creep!
Once upon a time (no more than 8 months ago), there was no analysis window as such. The corresponding window showed the move history, but you couldn't move the pieces about to try out future moves.
So we all said "Can we have a sandbox, please, where we can try out our proposed moves without having to keep a chess set by the computer? If we could just move the pieces about in the history window, that would be great."
So Russ gave us our sandbox, and we all reckoned that was great. It doesn't understand chess rules; it can't do pawn promotions and it doesn't hold any information except the game history it was loaded with and the current positions of the pieces. But it saves most of us with average chess brains from some terrible blunders.
If it could do much more, I expect it would take far too much bandwidth to send to our computers each time we click that link. Remember that one of the key ideas behind RHP is "nothing to download".
If you want a more sophisticated tool, you could download a program such as Winboard or SCID and use RHP's "get PGN of this game" feature.
Having said all that, I still wish there was a way of bringing pieces back onto the board, whether to undo captures or to show promotions. 🙄