The school you are applying to is a for-profit school that focuses on non-traditional college students. Most of those students have full time jobs including the military and are looking to go part-time; they aren't 18 year olds who just graduated from high school.
This means that your source of money from school is important. They are interested in students who have access to funds from their employer, or through the GI bill, or have enough financial stability to get a student loan.
If you were applying to a 4 year school where most students under 25, then work history isn't important; but with a school like the one you are applying to it might be important.
I would follow the instructions for that section. They are asking for all the employers you have had during the last 3 years. I have no idea if they will call references, but I wouldn't think they will. They are likely using it to evaluate the stability of your funding sources.