This came from a 15 minute unrated game of mine.  As usual, tell me if there's a mistake with the tactic.  (As a note, the moves for white are my opponent's responses.)

I think this correct.

I'm not sure I understand.  What happens after 4. Raxc1?

In a game, there exists a few degree of tactics. Sometimes, a tactic leads to mate, other tactics win material, and remains this one that only improve position advantage.

The tactic above improve material advantage.

what happens after Raxc1? Is that it?

After Raxc1, black can save the queen with something like Bd6 and be up a piece. That is the point of the puzzle, winning material, as cavalcanti explained.