What happens is that most games nowadays do their computations based on a timestep that's tied directly to framerate. Here's a good thread about this. The tl;dr is that lower framerates don't just mean choppier visuals, but also choppier calculations. This can affect everything from physics to input. That's why games that run at 60fps invariably feel more responsive than at 30fps. With a lower resolution you get a higher framerate, meaning more accurate calculations, and thus more accurate movement.