What is in this video is a direct elevator to an orbital asset that seems to be roughly in lower Earth orbit (LEO) region. This is not possible for the simple fact that the Earth spins far too slow to keep up with any orbital assets in this orbital region. As a point of reference: the International Space Station (ISS) orbits the Earth about 16 times every Earth day.
There is another theoretical space elevator type that is theoretically possible. This type of elevator has a "counterweight" tethering the hypothetical cable that would serve as the elevator. (For purposes of this post, I will not go into the complexities of creating such cables). This counterweight theoretically can be placed in a geostationary orbit (GEO). This orbital area is located roughly 35,000 km away from Earth. There, satellites can orbit at the same orbital velocity as the Earth spins. A satellite there would look to be always hovering in one spot from Earth's perspective.
However, many issues exist with his theoretical elevator:
First, you would need a massive counterweight inserted into GEO orbit to keep the cables taut. This is not a mass we can launch off of Earth. We would (more realistically) need to seek a massive asteroid to serve as this counterweight. We would need to find it - somehow move and insert it into the correct GEO orbit and at the correct velocity - and then tether the hypothetical cables to it. (All while making sure not to hit any of our geo satellites in the region).
Then we would have to periodically deal with boosting this asteroid - because orbital decay would be at play - and would effect our ability to use this elevator if the cables are not taught enough.
We would also be praying that no other orbital debris connects with the cables - because we would not be able to adjust these cables to avoid debris like we can with our independent orbital assets. If the cables we severed - this would be catastrophic on its own - not to mention being under the clock for dealing with a massive asteroid roughly 35,000 km away that will hit Earth if we don't "figure something out".
But even aside from this disastrous scenario - such a massive object in GEO would have a wide range of gravitational effects in our general region - from the Earth to our moon and anything in-between.
So why do this? For a space elevator? Idiotic idea if you ask me.