Sadly, this example of a Move-O-Graph "Live Portrait" is missing half of the image, which means that it no longer "moves." I estimate that it was taken in the late 1910s or early 1920s, merely by the hairstyle and moustache, but I could be well out.
I've found very few examples of this style of portrait on the net.
In an article entitled Animated Portrait Photography Stephen Herbert quotes another article published in the Amateur Photographer in 1916 in which Living Portraits are described in rather sarcastic and derogatory terms. He also includes an example from his own collection. I can't find many references to this style of portrait, so I presume that they never became very popular.
I've taken the liberty of trying to recreate the effect that this Move-O-Graph Portrait would have had by using an animated GIF. You'll have to be the judge of whether or not you would have wanted yourself preserved for posterity in this manner.
If any other readers have such Move-O-Graph portraits in their collections, I'd be keen to hear from you, particularly if their "movements" remain intact.
Herbert, Stephen (1989) Animated Portrait Photography, in History of Photography, Vol. 13, No. 1 (Jan-Mar 1989)