Little details from that scene on Gorkon's cruiser escape me, but didn't McCoy have a medical tricorder with him when he beamed over and didn't he wave one of his handheld scanners over Gorkon's wounds? A Starfleet medical tricorder circa 2293 should have had at least some Klingon anatomical data in its memory database given all the times that tricorders were shown to be able to access a ton of handy information even if they weren't interfaced with a ship's computer.
I dunno, it just looked and sounded weird and silly given that McCoy had 27 years of experience running into Klingons and that was just aboard the two Enterprises. He might have run into some of them even before he first joined the 1701 crew in TOS seeing as the Enterprise wasn't his first deep space assignment after medical school.
The movie's plot and pacing didn't require any of that, though, so it is what it is.