I am not 100% sure it's the NBC app. The Apple TV device works with I Pads, Macs, I Phones. We didn't get one for our bigger TV in our family room, just for the kitchen, where we usually hang out, so now we will get another one.
And yes, you can watch it any time. My schedule no longer permits me to watch it live every morning . We didn't have time to watch the 3 hours of racing yesterday, so we just watched the last half hour, during dinner.