games do not generally get very big. I have a game roo over my "yard candy" flock, and he is a wonderful rooster, but I would only eat one his size if I were REALLY hungry. He is a LF but is smaller than most dual purpose birds would be.
on the other hand, he is a great roo for free range, takes good care of his girls and keeps and eye on things, keeps the peace in the yard, also. His daughters are both fantastic broody hens, but they are also small, sort of wild, and tend to drag their babies all over the place -- survival of the fittest at it's most extreme
I lost a whole batch of chicks the one had hatched, because of rainy season and her desire to roam the yard/hayfield with them in tow.
I would go with a larger hen for dual purpose, but the rooster (if ya wanted the yard candy) might be ok to mix with them. The resulting chicks would most likely be smaller than the Mothers, but not, perhaps as small as the rooster.
as a side note, my game rooster (the yard candy king) looks exactly like the one in that pic - he's a super sweety, too.
meri