Now this is just a guess... I'm guessing 'gut driven' is referring to immediate actions that are driven by feelings
(possibly associated with memory). Specifically, I'm imagining external stimuli evoking an intense feeling associated with memory; as a result, one is prompted to spontaneously act on that feeling without logically considering other possibilities.
More accurately though, I'm guessing 'gut driven' is without reflection or void feelings associated with memory. In other words, 'gut driven' may simply be that one is
acting without thinking. For example, you feel like punching someone in the face, you just haul off and punch them in the face, lolz!