The video was pretty clear, and helped assure me that I was correct in assessing the inside v. the outside of the wheel in the diagram above.
I now think of backspace simply as the depth from the mounting face of the wheel to the inside rim. Offset is the distance of the mounting face from the centerline of the wheel--that is, the distance that the mounting face is offset from the wheel's centerline. If the mounting face is moved from centerline to the outside, it is positive offset (and gives a greater backspace), and if it is moved to the inside, it is a negative offset, and the backspace is reduced.