I think the issue was whether they were hunted to extinction or not
Yes they did, even if they were present in the continent before humans, they died out at least 10ky ago.
Also no sheep, no dogs, no cows, no chicken.
Native Americans did have dogs. They didn't have sheep, but the Incans did have access to wool-bearing animals in the form of the alpaca (though the Incan Empire was geographically isolated so these animals never reached North America). Guinea pigs were also domesticated in this region. There were neither cows nor chickens, but there were other forms of poultry such as turkeys and ducks.