A stove and and oven are not always the same thing in modern usage. Stove is frequently used as the combo stove/oven appliance, but is really just the cooktop portion. Besides, I can't think of all the terms that have been used over the years for these various appliances, not to mention the various national dialects of English.
Doing a bit of digging, the first fully enclosed stove wasn't developed in Europe until about 1735 in France. For practical purposes of the game, we're still talking about an open hearth here with possibly a tripod, built in hook, or a platform/stand for pots. (
"Early Kitchen Stoves") I'm not sure "stove" is the best use of the word to maintain immersion of the time period (from common usage seen in modern literature, not necessarily on classic definitions), either, though it certainly applies.
Edit: besides, shouldn't a stuffed turkey be cooked in a meat smoker?
2nd edit: Cooking large portions of meat over an open flame like this is very much possible. It's called rotisserie and has been a staple method of cooking for... well, I'm not sure anyone knows how long. (I'm sure someone does, but I did my research for the day.)