I disagree with the notion that the old rules were foggy on the subject.
18.2
a) OVERLAPPED – BASIC RULE
When boats are overlapped the outside boat shall give the inside
boat room to round or pass the mark or obstruction, and if the
inside boat has right of way the outside boat shall also keep clear.
Other parts of rule 18 contain exceptions to this rule.
(d) CHANGING COURSE TO ROUND OR PASS
When after the starting signal rule 18 applies between two boats
and the right-of-way boat is changing course to round or pass a
mark, rule 16 does not apply between her and the other boat.
18.4 Gybing
When an inside overlapped right-of-way boat must gybe at a mark or
obstruction to sail her proper course, until she gybes she shall sail no
farther from the mark or obstruction than needed to sail that course.
I think it's quite clear that the starboard gybe boat has all the rights in the world (but must not sail any further from the mark than needed to sail that course).