It's unclear to me what you're implying, but kills would always need to be returned to the group. For large animals, they would have done some degree of butchering and then returned the meat as manpower allowed. For instance elk, one of the examples they mentioned, can yield 300+ pounds of premium meat. Since our ancestors were probably eating/drinking parts we might discard, you can even substantially bump that figure up. That's going to feed an entire group of people for quite a long time.

For directions there's a million tricks to orientate yourself in the wild that they would certainly have been aware of. For a relevant one in contemporary times, the claim that moss only grows on the e.g. north side of trees is mostly true. A more accurate description would be that moss likes to avoid the sun and so tends grows to grow on the side of trees least exposed to the sun, which in the northern hemisphere tends to be the north side. It's going to vary by location/environment/etc but they would have known these things (and countless others) and so the environment itself would have been a living compass.

Apparently there's one tribe that doesn't even have a term for left/right/etc but instead uses solely cardinal directions. No idea if this is another bbc style claim or actually true, but it's at least completely viable.

There are countless means of preserving meat such that it can last months or even years - smoking, salting, freezing (naturally), the million ways of fermenting things - such as through burying, and so on endlessly.

Humans were quite good at preserving food before the invention of refrigeration, e.g. through drying and smoking for meat.

They could chase it in circles. Prey typically escapes pretty predictably (away from you), so you can chase from side to force some direction. Also if you have group, you can use everyone in group in loose circle.

Group can walk to the site. Butchering and preserving something like horse, buffalo or elephant with stone tools, is hard work, and takes a lot of work from everyone. Hunting is just a first step!

It was not like today, when "rest of the groups" sits at home all day, and expects everything on silver platter!