That's an "internal gear hub". It also takes some practice to do it quickly. In the video a small hex key is used to rotate it, not a spoke. You shouldn't need to adjust tension after re-install more than a couple of clicks on the barrel adjuster. If you do need to adjust at the hub, it does take practice which you normally won't get doing it only once per year..
They have a few advantages (basically zero maintenance over the life of a bike, can shift when stopped, easy to fully enclose entire drivetrain) and disadvantages (heavy, expensive, less efficient, can't shift under load, pain to remove wheel) compared to derailleurs.
They're nice for commuter bikes because you can fully enclose the drivetrain, keeping rain off the drivetrain and grease off of your pants and never need to be touched, until you have to remove the wheel, as you found out. Overall I think they make sense for that kind of bike.
They have a few advantages (basically zero maintenance over the life of a bike, can shift when stopped, easy to fully enclose entire drivetrain) and disadvantages (heavy, expensive, less efficient, can't shift under load, pain to remove wheel) compared to derailleurs.
They're nice for commuter bikes because you can fully enclose the drivetrain, keeping rain off the drivetrain and grease off of your pants and never need to be touched, until you have to remove the wheel, as you found out. Overall I think they make sense for that kind of bike.