After finding out that Rocky Mountain Goats have killed one person and have been known to harass hikers, how would you protect yourself from an aggressive goat? In most cases I would guess that simply staying a good distance away would be enough, but what if the goat decides to try and gore you?
The article you linked to seems to indicate that this is not something you need to worry about very much.
Rare and tragic events...
...potentially the first fatal attack by a mountain goat ever recorded.
...officials had known about this aggressive goat from previous reports...
...tissue sample testing might reveal disease or another reason why this goat was so uncharacteristically aggressive.
Mountain goats are not typically aggressive towards humans...
So this seems to have been a one-time tragic event involving an individual animal known to have caused problems before. To inform yourself, talk to the rangers in the area where you are going, and find out if they know of any aggressive individual animals.
Finally, they tell you one way to reduce the risk to yourself:
...they’re warning visitors to keep at least 100 feet away from all mountain goats.
If a goat still decides to be aggressive, then try:
...distracting it with an emergency blanket and tossing rocks at it.
Finally, if you do encounter an animal that seems aggressive towards humans, report it to the authorities (park rangers or others) where you are.