The moderately priced gym I used to belong to had classes for Yoga, Zumba, basketball, group weightlifting, hip-hop dance, water aerobics, spinning, barre, kickboxing, and a few other things. They have a dozen locations in the area so it’s easy to mix things up if you like.
I think what you’re describing could work and could fill a niche in the fitness area. One the one hand there are gyms where you’re pretty much independently working out and on the other are boot camp style workouts where it’s more like a team workout. The boot camps are kind of what you’re describing, but they are usually focused on high intensity workouts. The main purpose of people in boot camps is to get as fit as possible and having fun is a bonus. What you’re describing is a program where the goal is to have fun and get fitter. The fun part is one of the primary goals. In boot camps that’s not necessarily the case.
I could see that type of workout being great for the people who joined up. If you’re serious about this, contact the various boot camp workout groups in your city and see what they think. They might consider putting together a class like you describe and they would already have a marketing system to reach new customers. Try to find the larger boot camp groups since they would have the resources to add this type of class.