This was originally about cd players acting as gyros, right?
There are a couple of ways you can look at gyro action.
Let's say you take the front wheel off of your bike. You hold it by its axel and you move it around. Say you hold wheel so the disk like form of it is parallel to the ground. Now twist it a little off that horizontal plane and see how it feels. There's some effort to twist, right? Now do the same thing while it is spinning and the twisting effort is harder. In effect the spinning wheel is stabilized in space. It's not heading off across the room, but it likes to stay oriented where it is.
Now another way to look at it is when you spin the CD up or down there is rotational force imparted to it, a torque. If the wheel or CD spins in one direction, then there is an equal and opposite force or torque in the other. Not having seen the video, but I suspect, that if the CDs start up and slow down, the astronaut or some attached object can be oriented in space.
If you know what how the CDs will behave, spin at a constant rate, speed up or slow down, then you can orient the player or an object attached to it. You can point it in a direction you want it like a camera suspended in the air.
But you should not get the object to move ACROSS the room by changing the spin rate, unless you can push off another object with the reactive torque converted into a force.