I think Baba's struggle with the bear is more a symbol of Amir's own guilt toward his betrayal of Hassan in The Kite Runner. Amir relates the tale of Baba wrestling a black bear in Baluchistan with his bare hands in Chapter Three. Where such a story might be considered an exaggeration if another person was involved, few people doubted it since Baba was the participant.
And if they did, well, Baba did have those three parallel scars coursing a jagged path down his back.
Amir admits he has dreamed of this event several times, probably initially because he desires to be as strong as Baba (or the bear). When he does have the dream,
... I can never tell Baba from the bear.
But in a later dream while recovering in the hospital after his beating at the hands of Assef, the dream is conveyed differently. When Amir looks into his father's face, it is not Baba but himself.
He's me. I am wrestling the bear.
This specific dream spells the end (or at least the beginning of the end) of Amir's guilt for his betrayal of Hassan. He has returned to Afghanistan, recovered Sohrab, and returned alive. He has conquered the beast. Hosseini no doubt uses the bear symbolically and metaphorically, but I'm not sure that Baba himself considered this act of his past in such a manner.