(game meaf from necessary population control = ethical imo)
At what point do you consider population control necessary? The inconvenient truth is that the worst instance of unsustainable overpopulation is us humans. No other species could come close to the harm and destruction we cause. Making special exceptions for ourselves while we are the worst offenders by far would be very hypocritical. If you consider population control ethical, you ought to consider school shootings, murder, etc. ethical as well.
I think we need to find better solutions than going on killing sprees.
But all that applies to humans, and much more so. The harm done by deer overpopulation is completely and utterly dwarfed by the habitat destruction, pollution and climate change that our overpopulation causes. Based on your argumentation, hunting humans for population control is necessary and ethical.
But of course nobody will apply the logic consistently because of how cruel it would be.
Why don't we implement more humane population control measures for deer, like spaying/neutering? It might have something to do with humans liking the taste of their dead bodies...