You ran into one of the quirks of Utah liquor laws that is being phased out and hopefully will be gone by the time you guys come here. The state treats bars and restaurants differently. Restaurants are currently limited to serving 3.2 alcohol by weight (4.0 alcohol by volume) and only allowed to serve one drink after the customer has "stated an intent to dine". After that, yes, you have to order food to have subsequent drinks.
However, a bar is a bar is a bar even in Utah. Hopefully a lot of these laws are changed but if you visit in the meantime, just look for the sign at or near the front door indicating that the premises are licensed as a bar, not a restaurant. Yeah, that law is kind of stupid too but at least you can have all of the cocktails you want without any food and the beer is full strength, not 3.2.