A few thoughts off the top of my head.
1. The complaint about Paladins and Rangers seems really overblown. They aren't all any more magical than they were in previous editions; it's just that abilities that they had were shunted over to the same spell mechanic wizards use. Rather than having a "Hunter's Mark" special ability, they now cast "Hunter's Mark" like the wizard casts burning hands. But the ability doesn't actually feel any more magical to me.
It feels significantly more magical than 4e's
Hunter's Quarry to me. Oh, it starts off pretty much the same: a minor/bonus action, pick a target that you can see (4e's it had to be the closest, but 5e is less concerned with giving people incentives to move about in combat), deal a d6 extra damage when you hit with a weapon attack. We're all good. I like that it can last more than an encounter/5 minutes and grants advantage to attempts to spot or track the target, as that lends it some non-combat utility. I can even get on board with making it require concentration to maintain (which if anything, makes it feel *less* magical, despite that mechanic largely being used for magical effects in the system, as it evokes the idea that you're consciously focussing your attention on that target rather than having dropped some mystical target designator signal on them).
What makes it feel like it's a magical effect is that:
1. It requires a Verbal component. Rangers have to say something when they pick a quarry, and they are incapable of doing so if they are prevented from speaking, whether it be due to magic, environment, status effect, or temporary or permanent disability.
2. It's subject to all restrictions and limitations that other magical spells are subject to: it can be countered with Dispel Magic, it can be spotted with Detect Magic, it gets suppressed by Anti-Magic Field, etc.
3. It cannot change targets unless the current target is reduced to 0, or you recast the spell, whereas its non-magical predecessor could be changed once per turn regardless of the status of the current target. Note that this means that even if the target is clearly no longer worthy of the Ranger's focus due to having been removed from combat in some way
other than being reduced to 0, the Ranger remains fixated. The target is polymorphed into a newt, conked out with Sleep, and trapped in some way that it cannot possibly escape? It's surrendered on condition that no further violence be done to it? It's no longer even on this plane? Still your quarry, regardless of how many other viable targets are available – unless you'd like to expend another spell slot.
4. It uses spell slots. This means that a Ranger that uses enough magic spells in a day is incapable of selecting a quarry until he's had a long rest – and if he selects enough different quarries in a day, he's incapable of using magic spells until he rests.
Basically, if it can be detected by Detect Magic, uses spell slots, and requires you to speak a magical command, it seems pretty magical to me (or at least as much as anything else on the spell list).