Firstly what was the breeze strenght..... Your boat speed, their boat speed.

They obviously created an overlap at some stage but did they do it before the 2 boat lenght circle or after.

As Mike said, if you are coming into the gat on a Starbord rounding, the Port boat may have rights of an overlap and on a Port rounding the reverse is true with the Starboard boat holding potential rights.

Where it can get ugly is when a boat coming down on port heading for the port gate mark approaches the boat heading down on Starboard for the starboard mark. If they are going to their respective bouys, then it is a simple port / starboard. However if the Port boat intends to gybe and hails for bouy room, then you better be prepared to give it. After giving room though, the port boat MUST gybe and round or face committing and infringement.

If I was the starboard boat in this situation, I would yell "starboard" early and give the port boat an opportunity to call for "bouy room".

If I was the port boat, I would yell early "bouy room gybe rounding"