Do I need to use headphones with this entrainment technology?

Yes, if possible.

Our exclusive 3P DEAP technology utilizes both the left and right speakers on your headphones to deliver the binaural entrainment part of the technology. Therefore, it's highly recommended that you use stereo headphones to maximize benefit from the system. 

You won't need to shell out hundreds on a pair of headphones either. As long as you use decent headphones, which deliver the audio clearly and without distortion, the required audio entrainment frequencies will function just as well as they would on a more expensive set of headphones.