I don't know if they're technically game meats but I can buy them both commercially. Kangaroo meat is in most supermarkets, and Emu in speciality butchers.
"half emu & half pepper kangaroo, slow roasted tomato, charred peppers, lemon myrtle mayo"
It was good the last time I had it.
France's national bird is the rooster, it's not really a game bird but it's definitely eaten.
Pakistan and Gibraltar both have national birds that are partridges (the chukar and the Barbary partridge respectively).
India’s national bird is the Peacock. It is a type of pheasant and was historically a game bird that was a common delicacy, especially for the rich. It is now illegal to hunt peacock in India, but people still get it in the black market.