I'm not Ddawn, but I'll definitely answer your question unbidden (wink). No - I don't think that this gaping wound needs closing. As an ex-vet tech, I know very well that wounds like this, once closed, tend to be more likely to go bad than if left open to the air. Especially animal bites.
I agree that it doesn't look infected now. Honestly I feel it's because she's left it open. You can't see the microorganisms that are being fought by the body in that wound, however. So you simply don't close up animal wounds on birds. That's what our vet told us about any animal bite on any animal. And besides, the skin that you would use to do so isn't there. If there were deep tears in muscle that were the sort of gap you could stitch, like a gulley, that might be different. But this pretty much looks more bowl-shaped.
The fact that they're in dirt means one of two things. Either you remove them from their dirt environment to a clean mending place, or you cover (lightly) with a material that allows air in and keeps dirt out. In the case of this bird, it's in a difficult spot. The wound looks like it's being kept clean and the covering dressing keeps dirt from touching the wounds.
If she wanted to cover the wound additionally, she could possibly get a t-shirt, put it over the chicken, legs through the arm holes, and two holes for wings cut. Then gather the 'bottom' part onto her back and keep it gathered with duct tape. (Make sure you don't cover the vent.) You can gather the neck opening together a little more and keep it gathered (not tightly) again with duct tape. I child's cheap white t-shirt would work. They're washable, cheap, and very airy - keeps dirt out, allows the wound to 'breathe'.
I've had probably a half dozen wounds like this one in various places on chickens/ducks/geese/horses and made a practice never to have them stitched. The one time I did, on a horse, I ended up having a necrotic and very nasty wound despite twice a day cleaning, had to finally remove the covering (the vet did it), and once it was open it healed.
Granulating tissue will fill in the gape.
The problem with this one is going to be the possibility of a crop hole. The issue is whether or not to stitch it. As the bird is doing wonderfully, I'm not sure I would change a thing yet.
Just my 0.5 cents, again unbidden, but thanks for reading it anyway.
Good dialogue.