Horses aren’t on there so maybe the artist didn’t realize that they are a MAJOR source of milk in any horse culture. I can purchase mare’s milk cheese in over a dozen stores in this community.
Remember, once a tribe had corralled a bunch of animals in Springtime they'd milk females, select out the culls for slaughter and drying, lunched on a few young foals or kids, and then they'd turn the animals loose to go back eating the plants then growing freely on unsurveyed and enclosed lands.
People did that with horses, goats, sheep, donkeys, cattle, reindeer, elk, etc. They were "mighty hunters" already in command of the herds. Domestication came later as surplus vegetative matter suitable for animal feed became available. Then some tribal warlord figured out he could use people to feed the animals while protecting them from wild beasts.
Certain northern Africa cattle rearing tribes consume a blood and milk mixture, which they obtain by puncturing a neck vein of their cattle, and draining off a little blood. Apparently this is their primary article of food. Also I have read that if children stop drinking milk, they are likely to become lactose sensitive, but that continuing to drink milk into adulthood reduces the likelihood of developing sensitivity.