Frequently, playing the Scout in TF2, I hear this phrase:
What does the pally in this sentence indicate? Is it his imaginary friend? A paladin? Is it a nickname for something?
It means pal, like friend or buddy. Like saying buddy instead of bud, you can say pally instead of pal (or at least the scout does). It is not a reference to paladins or anything else - it's just a scoutism.
"Pally" is slang for "pal" which is another word for "friend." It's somewhat archaic, in that it would have been more common in decades past. It's fitting with the "New York"-esque aesthetic of the Scout's dialect.
It can also be used as an adverb to indicate being friendly, ie, "My neighbor and I were being pally by waving to each other while we were mowing the lawn"