If consciousness carries over then the only way to experience physical death would be to be conscious in your consciousness. Because when we are alive, our senses are constantly interacting with the world. They are constantly picking up information about our environment. I can hear the keys clicking. I can feel the smooth surface as I type. I can see the words being written. We are constantly glued to that information. If it's not sensory info then it's thoughts, mental images and sounds. You are reading this - skimming over words, maybe several words. Many trains of thought run inside your head. What are you thinking about? How important is it?
When we are alive, we are constantly attached to the senses and experience. We are constantly attached to some piece of information. But at death, these senses will leave us. No information matters there: no past, no future, no identity - "Na koi hindu na koi musalman". After death, consciousness, if it is present after death will be immersed in itself, without the senses. How would that feel like? What would it be like there?
This would a good experiment to try and perform in introspection, to try and be conscious of your consciousness alone without interference from sensory info or thoughts. For those who don't believe in any sort of after-life, just pretend for a few minutes that life after death is possible and that it's possible to experience that now.
The experiences that the man is talking about in the above video should make much more sense.