Adrenaline can just keep a body going way past any normal parameters, especially in endurance & strength.
That moose certainly wasn't a small one by any standard, being shot & having a dog right behind didn't help!
When you think of it dogs (domesticated wolves initially) have been doing just that for us humans for millennia, that dog was just using its instincts & herding the game back to the hunter!
Yes it wasn't a charge, but coming in like that & not dropping until right on top of the hunter certainly would have been an "OH SHIT" moment for sure.