Running doesn't require much cognition (imho), my body is on auto pilot and I forget time has passed - but I still feel like I get the beneficial effects from doing it.
In my experience, the cognitive load depends on the speed at which you're running.
Jogging at a leisurely pace, I don't need to consciously think about the jogging process at all and my mind is free to think about the books I have been reading lately, or to listen to an information-dense podcast, or to plan out the rest of my week.
But that all changes if I switch to running at near my maximum speed for the distance I'm going to run. Then understanding a podcast becomes nearly impossible and/or it interferes with the running. Indeed, having any internal, verbal 'train of thought' is difficult, other than my internal voice metronomically saying 'left, right, left, right' in time with my leg movements.
