I believe the significant difference is stance and steady shooting position required of the more deliberate rifle shooting. In doing this, my rifles are much more steady tucked in toward my body more, hands closer (the thing defining my LOP is shortest that avoids my nose getting whacked by my thumb). Also interesting that target rifles tend to have shorter stocks, I believe, for these reasons.
To the double rifle/dangerous game piece, I'm postulating that the longer LOPs are because of important factors: recoil and a style that is less about precision and more about speed (more like shotgun style). Can't fully explain it, as I don't own a double rifle. My .375, a custom bolt rifle, has a 13 3/8" LOP and it feels perfect and is very fast. Others may be about to add more than I on this point.