My guess, a visual approach, at night. The runway alignment for both airports is the same or very close. 15-20 miles out the pilot sees the beacon for the wrong airport and reports airport in sight. Is cleared for the visual approach and, following the wrong rotating beacon, lands at the wrong airport.
It was a night landing, just after 7 pm.
The ground track is interesting though, looks like it was heading directly for PTK (not BRG) before ATC radar lost it.
I wonder if they selected the destination airport in their avionics by name - Branson - rather than by identifier?
http://flightaware.com/live/flight/SWA4013/history/20140112/2145Z/KMDW/KBBG
It also looks like they got a direct clearance from the MAP VOR and bypassed the flight plan DGD VOR.
I bet this is when the avionics directed error occurred...:^)