Actually, people "like you" don't understand the meaning of the word "game."
Game only means "willing."
You're confusing DEAD game (game until the last breath) with "game" ...
Picked up "game" only means picked up "still willing to continue" ...
A dog picked up at :18, that's badly injured, but screaming for more, most definitely is picked up game ("still willing to continue").
YOUR confusion (not mine) is to think this somehow means the dog was DEAD game or "would never" quit.
The truth is, no such statement is said (or implied) by saying a dog was "picked up game" at :18.
The only thing that is said, or implied, is that, when the dog was picked up at :18, it "was still willing to continue."
And that's it.
Game just means "willing to continue" ...
DEAD game means "willing to continue all the way to the point of death" ...
Therefore "picked up game" is an accurate statement of ANY dog that is still willing to continue at the point of being picked up.
Jack