I made the same recipe, as I was looking for one without yeast. I cooked the pitas on a pan for 1-2 minutes on both sides, then placed them in the oven to cook. I did not turn them in the oven, simply placed them under the broiler for 1-3 minutes. They inflated properly, but when opened, one layer of the pita was super thin (the layer that inflated) while the other layer (you could say the bottom) remained thick and doughy, almost uncooked. My pitas ended up being under cooked, and I believe the reason for the doughy part is either from a. Having too thick pieces of dough/bread or b. not rotating the pitas in the oven, or not baking both sides evenly.
I made a second batch, added more water to the dough, rolled them out thinner and cooked them the same way. Though the bread was better, there was still the issue of the doughy part. That I believe can be solved by cooking both sides evenly, in my case by rotating them in the oven. Learn from my mistakes!