I worked for Westinghouse. We provided the fire-control radar and ECM pods for the F-16. I'm not aware of any guns that we provided.
Apparently, since I retired in 1991, the 20 mm version has been adapted to the F-16, at least in the Pakistani version, as #110 states.
In looking around, I was surprised to learn that the F-14A also carries the gun.
GE makes the Vulcan. "The Vulcan was carried on a wide variety of aircraft, including the A-7, F-4, F-14, F-15, F-16, F-104, and F-105."
If you look at the link that you provided, the gun has the capability of 6000 rounds per minute, but the F-16 carries only 511 rounds. That's a five second burst. Need to keep a light trigger on that puppy.
The Vulcan is also on a lot of Navy ships, for air defense. My son's ship, the Theodore Roosevelt had a number of them. No round inventory problem on a carrier.
All versions of the F-16 have always carried the M-61 Vulcan 20 mm Gatling gun. But of course the gun goes back farther than that. The B-52H once used it as the tail gun (earlier models had a quad .50 cal), and those came out in the early '60s IIRC. A-7, F-14, and other aircraft also used the Vulcan. The Army used it as a ground based air defense weapon, either towed or mounted on an M-113 chassis.