Andrew, I've been thinking more about the video, and here's my advice.
The basic video starts with an explanation of the Lab color space, which will be necessary to understanding the gamut plots in that space. Say nothing about where it comes from. Ignore the Cartesian aspect, and treat it like a cylindrical space, without ever using the term. Explain the lightness axis, hue angle, and chroma, giving them a consistent set of accurate but not too scary names. Then plot values for an sRGB monitor in that space. Animations would be good here. At a minimum plot the whole gamut and change teh viewing angle pointing out various features: the point at the bottom, the point at the top, the places where each of the primaries reaches its maximum value while the others are zero to form the three little tweaks at the upper part of the gamut. If you can do it, show animations of each primary running through its range, alone and in combination with the other primaries. Explain additive color along the way. Explain gamma if you want, but I think it's unnecessary and possibly confusing.
Then, with a wireframe of sRGB present for reference, show the results for an Adobe RGB display: just the gamut if that's all you have, and animations if you can do them. Point out that the sRGB gamut lies within the aRGB one.
Then explain what a working space is, and how it can be a real or idealized monitor space. Then show PPRGB's gamut. This is a little tricky, since PPRGB has a different white point than either of the other two spaces, and white point translation is beyond teh scope of the video.
Then show a couple of printer spaces, and point out how they differ from monitor spaces: more chroma available at lower L*, less at higher L* except for yellows, more dark cyans available, etc.
Plot both sRGB and some inkjet space, and show where the printer's gamut exceeds sRGB, and vice versa.
Pick an image in a biggish space, and show the gamut of colors in it. Show what colors can't the printed, and what ones can't be displayed in sRGB.
I think you can take it from there. The difference between changing color spaces and just changing profiles, for example. No chromaticity diagrams. No discussion of linearity. No information on what goes on under the covers when you change color spaces.
If people are interested, you could do a companion video: introduction to the eye, cone responses, the color matching experiment, XYZ, xy, the ellipses, u'v', monitor gamuts in u'v', opponent color (to prepare them for Lab), Weber's law and nonlinear luminance response, Cartesian Lab, cylindrical Lab, color differences, and an optical illusion of two to show that it's not all about point color.
Jim