With the ‘Move’ tool active, hit Ctrl once to get the + sign to indicate that you 'll move a copy of your selection.
Same thing applies to the ‘Rotate’ tool, hit Ctrl once to see that + sign at the cursor.
To rotate (a copy of) your selection, press and hold the L-mouse button at the center of rotation, (first clicked location). Now still with the L-mouse button down, drag the cursor to the desired location (some vertex or along an axis or whatever location) to set the axis of rotation. Only then let go of the L-mouse button.
Second click is the starting point of the rotation angle.
Third click is the end of the rotation angle.
In the beginning of @Box’s video both these two clicks are the corners of the rectangle. (avoiding the flipping into the wild)
Previously the axis of rotation was set (dragged) along the green axis
You may want to look at your model from a slightly different angle to better see what you are doing. You don’t need to make that video like Box does. He needs a “stable” view without hopping around.
There are no tricky key combinations involved.
The last rotation of the two curves don’t need that “drag to set the rotation axis”. The protractor is blue ‘on face’. You only need to subcequently find the two midpoints (top edge and right edge) to set the first click in the center.