Gaminess

Thanks for posting this. It's definitely something I've dealt with regularly. I genuinely think that a lot of that "gamey" flavor people taste is blood, but there's unquestionably more to it. I've noticed a similar taste in domesticated animals that weren't given the full dry aging that beef typically gets. If you don't want to know that you're eating an animal, then you probably shouldn't be eating it.
That said, venison is my favorite meat.
I think the "AP view" is a misnomer with the typical qualifications. There's such a range on individual responses that there's no reason to pretend that your view on hunting or not hunting speaks wider or louder than most.
So, from my own perspective, I have no issue with subsistence hunting. Like everything, there are limitations: don't be stupid. If you think you need to eat Black Rhinos to survive, then you should probably check the news on that one. But hunting, like eating meat, is a primordial act. Likewise, there are plenty of technological distractions that can erase the sacred from the process pretty quickly, but there are plenty of old school hunters who understand the implications and connections of hunting without having read any Paul Shepard. There's an instinctual thing here, it's just a matter of listening.
So "our context" is equally problematic, but I know that you mean while living in a civilized nightmare where meats are readily available. Let me say this much, I totally get why someone wouldn't want to eat meat if it meant taking part in the agricultural food system. That makes complete sense to me. While the meat industry directly takes lives and adds that element into the equation, it's ridiculous to think that any level of food production doesn't have equal to or more blood on its hands. If you want to step outside of that, then there's a clear path there. Taking a life is a big step for many and one that can be easily avoided by just picking up roadkill (though there's been heavy competition on that front since even before the recession).
When it comes to subsistence, I think this is an important step and removes a lot of mediation and garners a lot of respect and admiration when done correctly, but I'm not saying it's a step that anyone should take unless their ready. It's not one to be ignored nor taken lightly.