No, they admit people without a BS in CS but I think they want to make sure you'll be able to succeed in the program. So it helps to have professional software engineering experience or some other coursework.
I take that to mean that you need to have a bachelors in something. Econ is a relatively quantitative field, so that with work experience is likely acceptable.
I'm currently in the program with a BS in Industrial Engineering. I highlighted the CS side of my job in my application, and had done a lot of learning on my own time between my BS and application. So it's definitely possible if you're interested.
http://www.omscs.gatech.edu/program-info/admission-criteria