It's good that you're apparently keeping in mind that the organ, even the King, the pipe organ itself, is a wind instrument. The earliest verifiable construction/use of an organ comes from the Roman culture, c. 200 BCE. Apparently, some genius felt like playing his pan flute wasn't getting the job done, so he built a giant set of pipes (giant compared to your standard pan flute, not compared to your standard pipe organ, of course) and rigged it with levers and a set of bellows.

As for the Authorized Version of the English Bible, the translators just wanted to mention instruments its initial readers would recognize. All about making sense to your audience, really. Sort of like when the Caesar in _Gladiator_ signals an execution in the Colliseum with a thumbs-down sign--EVERY historian knows that was always signaled thumbs-up, but this wouldn't make sense to a modern movie audience, so it was changed to reflect the current connotation, rather than the original.