Last I checked deer numbers are has high as anytime in the past, maybe even more. There are less predators (they can eat humans so we don't want them around) and deer have figured out how to live around humans just fine. Deer numbers were way down in say 1960 (as you say they were hunted to near extinction) but with stronger hunting and environmental laws they have come back.
Of course hunter/gather lifestyles never supported large concentrations of humans like ag did.
Deer are an outlier. Most other game species (like buffalo, elk, bear, beaver, various birds and fish) have seen significantly reduced number and fitness relative to pre-1900 levels. “Game” in my previous comment was referring broadly to any animals hunted for food or other sustenance (e.g. pelts, oil, etc).
Right, most of what you list either hasn't figured out how to live with humans, or is a predator that will kill humans, so humans kill them (illegally!) or otherwise chase them out to protect their children.
Of course hunter/gather lifestyles never supported large concentrations of humans like ag did.