This is a tricky situation with small gates.

If you are outside of the 3-boat circle then simple port/starboard rules are in effect.

If you are inside 3 boatlengths of either mark, then Rule 18 (Mark-Room) takes precedence.

Assuming you are inside the 3-boat circle, then:

If you had continued on port towards the Left mark, the starboard boat would have rights as the inside boat and be entitled to room at the Left mark, and that includes room for a takedown and gybe around the mark.

However, had you gybed over to starboard and gone for the Right mark, you would have been entitled to room at the mark as the inside boat. He would have had to do a takedown and round outside of you.