You can do this.
My friend Jeff and I used to do this all the time, although we could only do it laying on the bottom of the pool and the rings would only go up. Basically you puff the air out really fast, with an abrupt stop. Having your lips really tight helps. The effect has more to do with the water in a toroidal vortex and air stuck in the center of the ring.
When we did it upwards, the force of the air going up I think was enough to draw water up through the center, initiating the vortex. As the air rign thinned out and expanded, possibly from decreasing pressure as it traveled up, it would grow more unstable until it collapsed into a ring of individual bubble that just went straight up.
It looks like the dolphins are able to expel some air and then pierce it with a jet of water, and create the vortex in any direction. Then the way that they manipulate it is amazing.
Very cool.