I've taken the Sirius Puppy classes with my last 3 dogs - Dena, Keefer, and Halo. They were created by Dr. Ian Dunbar. The classes are almost entirely off leash (unless we were specifically working on leash skills), and the short play breaks during class were actually used in the training. Since I do most of my training at home off leash, or I may attach a leash to the collar but then drop it on the ground, my pups are used to paying attention and working with me off leash, even around the distractions of the kitties, for several weeks before we start puppy class.
Some of the things we'd do is release the puppies to go play, and then go up to them and ask for a sit, give a treat, and then release to play again, or we'd lure into a down, or just do a collar grab instead of a sit. The idea of course was to get them to be able to focus on us around the distraction of the other puppies. We worked up to calling our puppies out of play to come back to us for a treat. If any puppy did not come to the owner everyone else was to hold onto their puppy, so there was nobody for the puppy to engage with, while the owner approached and lured the puppy towards them. And playtime wasn't a free for all, we were all responsible for monitoring play and redirecting the more boisterous puppies away from the less confident ones, until they felt more comfortable.
With Keefer I actually had a hard time getting him to leave me so I could call him back - he was WAY more interested in the treats I had than he was with the other puppies in the class. Halo was pretty distracted her first week in class and didn't do that great, but by week 2 she was doing off leash down stays with treats on the floor in front of her. And she had a rocket recall out of the play breaks, she'd spin on a dime and charge right back to me!
In Dena's Puppy 2 class we worked on downs while the instructor and assistant went around the room trying to distract them with balls and Kongs, rolling and bouncing them past the dogs. Since that was a difficult exercise, when it was over the dogs were released to go play with the toys for a few minutes. This was great impulse control work, and basically the Premack Principle - ignore that ball rolling past or that bouncing Kong and you'll get to go play with it later.