The way I usually do this is to hold CTRL, click one of the opposite handles (not diagonal in this case), then scale the part to an arbitrary distance manually, then let go of the mouse button and the CTRL key, then type the measurement, followed by Enter.
Scaling about center seems to work a little different to normal scaling as you are unable to enter dimensions with the CTRL key pressed. If you started the scale and let go of the CTRL key to enter the dimensions, the normal Scale tool is activated again. That could be what went wrong.
If Im honest I would prefer the “Scale about center” modifier to be a toggle so that it stays on or off, rather than have to hold the CTRL key down. Much like how the modifier for the Rectangle tool works. But that’s just me, there’s probably a good reason it doesn’t work that way.
Toggling modifiers would be good but you can still get on without out it for the Scale tool. The trick is to let go of the mouse before releasing the modifier key.
As for the tutorial, it’s a cool trick but I would have used a corner handle instead of scaling in two steps.