No restaurants in the park. Take any special food you need with you. Local Kazakh foods are generally meat and...more meat. Goat, sheep, horse, camal and cow.
You will most likely "go native" and eat with the locals. It's customary, and generally a nice thing, to bring some onions, potatoes, carrots, cabbage, a bag of noodles, rice, as food items you can give to the woman of the house, who mainly prepares all meals. This is easy if you've hired a car and driver for your trip. You can get these items in any quantity at the local Ulgii open market. A really interesting place to go. Watch your pockets though! Your driver or guide can help here. You'll also want to take along bottles of water for the ride. You can find these in many Ulgii Center shops. Also bring any herbs, tomato sauce, or soy sauce to help make the food tastier to your personal preference.
If you are really staying with locals in the park, it's also nice to give a needed household item as a token of your appreciation. Candles, packets of matches, a small a block of green tea, and of course a handful of boiled sweets hard candy for the table and kids. It's not mandatory of course, but a nice gesture. You can get any of these items at the open market as well and in any quantity you want.