Dangit, tried to edit the comment to amend my theory and managed to delete it instead. :/ Edited version was meant to read:

I got the impression the Barely Breathing Deer was a real deer, but empty. It "caught" the BBD, “ate” its soul or conciseness or whatever, and was waiting to use it as a lure to ambush the humans.

That’s why it was just off the Human Game Trail, that’s why it was pulled so close up against a tree it had a hoof on the trunk, and that’s why when Grandad tried to startle it with a clap, water fell off the leaves and branches directly over its head in perfect time with the head turning.

Whatever the fuck is hunting them, I don’t think it’s shapeshifting. I think it’s using the empty bodies of the other things it’s caught like decoys, and turning the deers head required some kind of movement on its part, like controlling a large marionette. But they didn’t go up to the deer, they went wide around it - so it couldn’t Death From Above them.

Wonder if it uses the deer as lures for other things beyond humans, like bears or mountain lions.

Hey OP, the Shadow is an inverse of human hunters, but uses the same techniques!

Humans discard the soul to consume the flesh, the Shadow seems to discard the flesh to consume the soul.

• All the animals are like empty vessels - still breathing, but void of other markers of life. Standing, but catatonic. Upright and coma-like.

Humans use decoys made of foam and fiberglass, the Shadow uses decoys made of flesh.

• The deer in the lake show “idled vehicle” behavior; like the original they’re empty vessels, but have clearly been transported and stored for later use. Perhaps the lake storage was meant to keep them cool and keep the flies off them; humans have used lakes as refrigerators before so why not the Shadow?
• Grandad admits he doesn’t know whether Steve is alive or dead, which implies he saw Steve in the same state as the deer, way back when. Otherwise, it would make no sense for him to even consider the possibility that Steve might be ‘alive’, as Steve was lost to the woods and the Shadow years ago. But if he saw him like the deer, it makes perfect sense to not be sure if ‘Steve’ is alive (but in a trance) or dead (but still breathing).
• This also explains Grandad shooting wide at the end: He really doesn’t know whether the Steve he knew is still in there somewhere, or whether he’s gone entirely. He can’t risk killing his friend if there’s a chance Steve isn’t just a meat puppet for the Shadow.

Humans use calls to lure their prey, the Shadow uses calls to lure their prey.

• It serves to reason that the Shadow didn’t use Steve’s voice against Grandad because it recognized him; it used it because it thinks that’s what a human call sounds like, and being in the deep woods it’s likely the only ‘human call’ its learned beyond Grandads. And when it used Grandads, you (the OP) didn’t come out right away, and when you did you checked on him and went back to sleep rather than moving away or going for a walk, etc.

Humans use camouflage to disguise themselves and prevent prey from ascertaining their true form, the Shadow uses camouflage to disguise itself and prevent prey from ascertaining their true form.

• When y’all come upon the Shadow in the clearing, you say you know something is there but can’t bring it into focus, that the branches and leaves and shadows seem to be moving. This is how human camouflage is meant to work on animals - to break up the form, confuse the eye, and seeing only moving leaves or branches (if you shift) is supposed to be less alarming to prey.

Humans tend to use all these things in concert with one another, and so did the Shadow.

• In the clearing, you come upon the Shadow having set up a hunting spot.
• It has pulled the only Human Decoy it has, Steve. We can assume the decoy is old based on Grandads comments, so the Shadow has smartly positioned it under the canopy where you can’t tell if it’s a bit beat up, decayed, etc.
• It has camouflaged itself behind the decoy. If it was capable of ranged attacks the way a human hunter with a gun is, it would have been able to attack from there, but instead it starts moving closer. Whatever it really is behind the Shadow camouflage, it’s a melee predator and it needs to be VERY CLOSE to attack, but the need to be close to attack seems to be causing the camouflage to interfere with the decoy it’s using to try to lure them in.
• It uses the ‘human call’ after the decoy gets their attention. Probably hoping it makes the decoy more convincing, just like human hunters. Possibly hoping humans were highly territorial, like bucks and bears, and would rush the decoy thinking it was a rival.

If we go back to the beginning, we can see one more hunting technique: using a game trail.

• The human hunters are making their way through the forest, and I believe at this point the Shadow is tracking them from behind. They startle the deer, who flee away, then towards, then PAST them and back the way they came. The first deer is ‘caught’ when it flees in the direction they came from, because it runs right into the Shadow that’s been following their trail.
• As they head back, they encounter the first deer just off the same path they took going out. The first deer has one hoof on a tree trunk; so we know it’s standing almost right up against a tree. When they try to startle it, water falls off of the leaves that are directly above it as it turns its head. That’s because the Shadow is there, in the tree above, controlling the deer and ready to pounce if they approach the deer it’s using as bait.
• Luckily, Grandad tells OP to go wide around the deer. That the Shadow doesn’t try to jump down and rush them implies that either it’s extremely slow (unlikely), or is so specifically an ambush predator that it doesn’t have the instinct to just chase prey that moves away.
• I think something similar happened the night before they left. The Shadow - possibly using a decoy, possibly not - rubbed against the tent, and used a ‘human call’. - When OP comes out and starts checking around, he says something chirps. Just once. But he doesn’t see what chirped. This is likely the Shadow again, trying to lure him out to where it waits, camouflaged.
• There is a second chirp, which comes only after he’s checked his grandad, stood up, and given the woods his attention again. This is the same thing that happens the next day in the clearing: When they focus their attention on its lure, it calls.
• It fails at this point; the humans are not interested in deer decoys and bird calls. They do not come closer.
• But the one ‘human call’ DID get the human out of its den, eventually. So humans respond to humans. Perhaps they have to be lured with human calls and human decoys.
• Hm.
• I guess the next logical step… would be to use both…