Ah yes, that makes much more sense. Lower shutter speed = less light on sensors per frame!
When you lower the resolution it allows more of the sensors to be dedicated to a single pixel. Along with reducing noise due to magnetic interference.
Say you're taking a video at the maximum resolution. That would be the space on this sensor dedicated to a pixel.
Once you lower the resolution by several factors, it increases the surface area of the sensor dedicated to the pixel, allowing the light entering the camera to stay constant. (aka, no forgeted up exposure)

This matters a lot in video camera that also run at an extremely small aperture, such as phone cameras, camcorders, gopros, and the like. When you lower the resolution of pictures so much more of the sensor can be dedicated to taking in light for single pixels, which helps vastly improve the problem of noise and lack of light when taking video at higher framerates.
Cut resolution in half, get double the frames. easy.
EDIT: Shutter speed is irrelevant for taking video. The shutter stays wide open while filming.