Blurry Videos While Walking when Image Stabilization is set to Active

This issue can occur when Electronic Image Stabilization is set to Active.
Electronic Image Stabilization corrects blur by adjusting the position of each frame through cropping, but it cannot correct blur during the exposure of each frame.
Therefore, if the shutter speed is slow, the blur during exposure may appear as a blur in the image.
Try setting the shooting mode to either Manual Exposure or Shutter Priority and set the shutter speed to around 1/250 second to reduce the blur. 
Keep in mind that faster shutter speeds can make the video look choppy, so adjust the shutter speed to balance blur.