Just FYI, chicken feed is only 2-4% less protein than a game bird feed, so they would probably survive just fine on it. Notice I said "survive", not " THRIVE".
Problems with bone growth, nutrient assimilation, building blocks of amino acids in protein rations. Slow to grow, maybe. It actually depends on if they're meat birds or breeding stock. Meat birds can be packed with protein with no regard to longevity because they will be slaughtered before maturity. But breeders need better nutrition to form good strong stock in the eggs.
It's not just the protein, but the composite of protein, fiber, energy, fat, and vitamins to take into account. Balanced is the point if they are going to be able to absorb all the nutrients.