Clearly somebody has not heard of hydraulic elevators. make me wonder what other obvious things were missed.

It reminds me of the turbo lift on the Enterprise (Star Trek). It seems another tech from the television / movie series becomes reality.

Long on showmanship, short on technical details. Also, you could stick multiple elevators into the same shaft if you were prepared for each one to service only a portion of the shaft, say floor 1-20, 21-40, 41-60 etc, and that without much change on the current system. Also, new elevators doesn't mean new buildings, buildings are built as they are because it combines safety and efficiency, not because we got stuck with the wrong elevator.

now finally my dreams (real ones at night while sleeping) have come true.... on a number of occasions I dreamt being on board of a elevator that went up and than across from buildings to others.... was very weird but almost real! sweet dreams.......!!!

Fail to see how this would increase available floor space by 25%. The elevator cabins would be smaller? What if there is a power failure? A Maglev train just sits there, but what happens if you're in a vertical shaft?
Still, the concept is intriguing and not simple, with some potential for people who can't bear to wait one minute longer!

I cannot think of better way to ensure that a small pocket of fire gets every chance to spread rapidly throughout a building and kill the maximum number of its occupants before they escape. It deserves a prize.
In the meantime, one could run a sweepstake on how many get jammed each time the power goes off and catches them transiting from vertical to horizontal movement.

This concept has been anticipated by various man-lifts as well and science fiction, as in Star Trek.
Still, it has a lot of promise. I can see a large saving with multiple cabs. coupled with vertical and enough transverse shafts that a large building can have , say 4 vertical shafts and in the AM rush can use three to take people up and one to go down, with transverse travels to bring empty cabs down and move them to up shafts. At days end, the reverse is true. They could also park some empty cabs in dead ends, to save energy and wear and tear - as they do in subways and railways now.
Cab shafts will need enough battery power to descend in safety. In fact with Tesla style battery packs, they could store enough power to operate an evacuation, and regenerate on any descents,and gradually reduce the cabs in use as the building empties, so at the end only one still runs = longest emergency power life.
Cab would also need the ability of a fire crew to wheel in a battery to power one cab upwards to whatever floor, with descents used to regenerate the battery. This would bring an ability now lacking in power failed elevators. These cabs can be lighter, they need no counterweight.

@Slowburn
AFAIK hydraulic elevators are for different use. Usually only for a few storeys. They have their advantages, but their main drawback, especially in higher buildings is they don't have a counterweight (or at least something similar in function). This means they always have to move the whole weight, not just the difference between weight and counterweight (and the friction in the system), as cable elevators do.

It will be interesting to see how architects will take advantage of these elevators when they become available. I don't see any potential problems in the preceding comments that are not easy, if not trivial, to overcome.

This is nothing new - Willy Wonka had one. Did it take this long for someone to find a golden ticket and sneak a peak? Probably could have saved a lot of time and bribed an Oompa Loompa. Does this run on chocolate and dreams?