What you feel as weight while standing on the ground is not because of gravity but due to the normal contact force applied by the ground on you. When that support is removed you won't feel your weight.
If you are hanging in space with nothing to apply force on you then you are not going to feel your weight.
And When you are falling under gravity with nothing to counteract your fall or say apply the contact force then also you won't feel your weight and that's why we say both the situations as free fall.
So both are related as in one there was no force and in the latter there was no support or contact force. So both the situations la kwe lack the normal contact force.
This is exactly what is exactly explained in your linked video.