It used to be illegal to carry a handgun in the park. Now maybe some of the people who whined about legalization will see why it's a good idea.
This goat was a Rocky Mountain goat (o. americanus). It's a darn sight tougher than a barnyard billy, and goes about 250# on the hoof. Elmer Keith once emptied a Colt SAA in 45 Colt into one at close range before dropping it. I think Boddington's "American Hunting Rifles" suggests a 30/06 with 180's for hunting them. In a handgun, I'd want a 250-grain (or heavier) hard-cast slug at 1,200 fps.
In the end, poor tactics got this guy killed. Another report about this incident tells that two women were ahead of the party that got attacked. They met the goat first, but retreated after it challenged them, and warned the guy who got killed that there was a problem ahead. They did the right thing. He did not. So tactically, I think it makes more sense to withdraw after the warning than to pick a fight with a wild animal in a National Park. Without a warning, I think you shoot once the goat gets to within 10-15 yards.
Okie John