Normally, "recommended" means that you don't HAVE to use it. If they were serious, they would come out and say "required" like a lot of other automakers do. But preimium is what Mazda used for their horsepower and 0-60 tests.
This car has a knock sensor, electronic ignition and variable valve timing. It can dial back the timing to prevent knock or ping. In order to get the most power and acceleration, then, yes, premium is what you need. But if you drive in an economical way on reasonably level ground in moderate weather, something less than that should be OK. But don't buy the cheapest off-label stuff you can find, either.
Confusing the issue is the fact that premium is only 91 in most of California, but can be as high as 93 or 94 elsewhere.
Miata.net is a spirited board visited by a lot of Miata owners. Read the link below to see what other owner's have said.