There may have been other factors involved in the demise of the passenger pigeon, like habitat loss, particularly with beech trees (which they were heavily dependent on) being removed for agriculture. It's been suggested that there may have been a disease ffactor as well, because despite the fact that they were overhunted, their disappearance was rather sudden, as well as total. So who knows.
Nevertheless, the hunting of them was rather heavy. Same with others, like the Carolina parakeet which even early bird watchers shot by the flock because that's what they used to do back then during John Audubon's day. Audubon himself would literally shoot bunches of whatever bird, just to paint the image of one. Carolina parakeets had the bad habit of coming to investigate when any of their flock were in peril, making them easier targets en masse for someone with a rifle.
The end of the Ice Age/10K mass extinction date is really quite a bit off, I have no idea why scientists keep referring to that as some sort of magic number when it's nonsense. Most of those animals became extinct thousands of years after, some before that as well. You've probably heard of dwarf woolly mammoths surviving on Wrangel Island till 4500 years ago, but they've actually found Mammoth DNA in Alaskan and Yukon permafrost dating to around then as well. They also found DNA of one of the giant bisons, Bison latifrons dating to a mere 450 years ago. That's right, 450, we came this close to seeing them.
There's evidence that humans coexisted with other Ice Age megafauna for thousands of years. So it wasn't this blitzkrieg killing event that some have suggested. I had read some years ago that the killing of just 5% of mammoths per year would be enough render them extinct over time, but not overnight.
Regardless, all these species were doing fine until after the arrival of humans. Once humans get hit the scene, species start to decline. We've seen this also in more recent times when people got to anywhere from Hawaii to Madagascar. And it wasn't just hunting. There's habitat degradation, particularly with the use of fire. Most grasslands on Earth, for example, are anthropogenic. They're created by humans periodically setting fires. It's happened on the mass scale in North America, for example, creating the Western Prairie. Yes, that quintessential American ecology is man-made.