Probably similar to the Neanderthal diet.
Probably pretty much whatever they could find that didn't eat them first.
Whereas the reconstructionist was analyzing southwestern Natives who lived near a river, hence the cactus, fish, and various desert plants. Even in a desert, there's a lot of useful plant food -- more than the ancient mammoth steppe. However native diets, before agriculture, were ALWAYS high in animal products, in ALL parts of the world, even the warmer areas.
Interesting reading: Guts and Grease -- the Diet of Native Americans. Paleo-European diets were similar.