The only reason the conference HQ was in Providence is because the AAC is the successor entity to the old Big East, so the office there automatically became the AAC office. It was there because Gavitt, Tranghese and Marinatto were all part of the "PC mafia" that ran the conference. All of them and a bunch of other employees all came from the PC athletic dept. administration.
I'm guessing none of them could figure out a way to get out of a long term lease agreement for the office space there. They've just been waiting for the lease to expire so they can bolt. Considering there are no longer any ties with PC and no other reason to be in Providence, it was inevitable that they'd move the conference office.
Moving to Dallas certainly seems to symbolically represent that Aresco now considers the true power base of the conference to reside in Texas, with SMU, Houston, Tulsa, Memphis, Tulane and Wichita St. all in close or relatively close proximity...a less than one or two hour flight to any of them other than SMU, likely without having to change planes. Dallas is a major transportation hub.