I am wondering if I should post questions about cooking game here, or put it under the cooking SE? For elk and venison, there are a few questions with answers there, but for duck and goose, it is hard to tell the wild from domestic questions. I see utility in allowing the questions here under the hunting tag because it also is more likely to be seen by the relatively few people who eat wild game and less likely to be seen by those who might wish to discuss the ethics or aesthetics of eating game rather than the actual question. All that said, it is cooking. Any thoughts?
I pretty much agree with both answers, but want to introduce an additional aspect, which is the complexity of the cooking.
If the OP is asking about elaborate recipes, with sauces and garnishes and/or the courses and wines that would best complement the game course, the question belongs on cooking.
If the OP is asking about how to simply or safely prepare, e.g., elk tartare, it belongs on TGO. Similarly, if you have a lakeside cabin and want tips how to simply prepare the day's catch, it could be on TGO.
Cooking game while outdoors (camping, backpacking, etc) = Outdoors
Cleaning/Dressing game taken while outdoors for later cooking = Outdoors
Cooking game in your home that happened to be obtained outdoors = Cooking
The last one is hard for me. How to best cook [insert game] is a very common outdoors topic even though it is often cooked indoors. However, I think while it isn't necessarily bad here, it is even better suited to Cooking.
If you slaughter, cut up, and cook an animal while you're still somewhere in the jungle, it belongs on Outdoors.SE.
If a rented helicopter has kindly transferred the carcass of your freshly “harvested” moose to your truck/trailer and you've managed to put the carcass in the giant freezer of your luxury lakeside property, and you're presenting bits of it to guests three months later, it belongs on Cooking SE.
The reasoning here is that the indoor cooking food obtained outdoor is not an outdoor activity, nor is it preparation thereof, just like how editing photos obtained outdoor is not an outdoor activity.