Starboard/port tack only applies to two vessels under sail...
See Rule 12.
Rule 15 doesn't have anything to do with this situation...it says that in a crossing situation, the boat coming from the right (starboard) does have ROW...which is no different from the rule on land that says the vehicle coming from the right has ROW at an intersection.
Regardless of whether a vessel is under sail or under power, the overtaken vessel has to be the stand--on vessel....'cuz suddenly changing the conditions that existed when crossing or passing began creates problems for the overtaking vessel. But actually that applies to BOTH vessels equally.
Which means that sail isn't always stand-on...another example, happened to me: I was hauling down the main channel of Lake Lanier at about 30 knots. Lake was like glass...not much wind...sailboat ahead maybe half a mile, a hundred yards to starboard and drifting to starboard. No problem ...I'd cross at least 100' behind him. Except he suddenly came about and headed straight for me when I was less than 100 yards from him...which produced the predictable "Oh $#!+" at my helm while executing an immediate 90 degree turn to port!
Even though I was power and he was sail, he was obligated to maintain course and speed till after I'd safely crossed behind him, and so was I...UNLESS he was so close to shore or a shoal that he had no choice. In that case it would have been up to me to be aware that he was about to have no choice but to come about and alter my own course in plenty of time to give him the room he'd need. But that wasn't the case here OR there.
The Rules that cover all this are 13-17...and ya gotta read 'em all to put together who's stand-on and who's give-way.
Btw...my sailing friends taught me early and well: always cross behind a sailboat, and always pass on the lee side.