MDW-LAS is a long haul for a 727 these days, particularly those which employ "procedural" hushkits to make Stage III. Perhaps the westbound headwinds were significant enough that the boys decided to land for fuel. (Had it happen myself once on Braniff a long time ago from NY-DFW; headwinds required us to land and refuel in (I think) Memphis.) On your BOS-LAX flight with ATA, you'll have a nice 727 from BOS-MDW and a 757 from MDW-LAX. The 757 has plenty of legs; it's not even a little stretch to get to LAX on one out of MDW, so you will not have a fuel stop.
By the way, ATA's equipment is generally quite nice inside; they make a big deal out of thoroughly cleaning the cabin on turns and at MDW. The pitch is comparable to everyone else's, and the service is generally quite good. They'll happily give you a full can of soda, they seem to care that you have a nice flight, and you even get a little snack and a movie on the MDW-LAX leg, which you don't on most of those carriers flying smaller a/c on that route. ATA will also be replacing its 727s, starting early next year, with 737-800s. ATA is the launch customer for the maximum-performance 737-800, with factory-installed winglets, and they are buying them *loaded*, with heads up displays in the cockpit, extra-powerful engines, etc. And they are installing seats with better-than-average pitch, as well.
You will enjoy your flight. I have taken them many times in the past year, and enjoyed every flight.