Sorry this might go long and off topic.
Thanks for finding that. I've been sharing an older Anna-Maria video with friends for years, but this one is incredible. I've never seen the overtone series demonstrated so cleanly and visually.
As a brass player I'm well familiar with the overtone series and the partial series, which are slightly different on trombone, but it's a distinction that most wouldn't be interested in.
The driven overtone series on trombone has a very simple mathematical relationship. The octave is exactly twice the frequency, and the others have similar integer multiple relationships, as do any "perfect" or beatless intervals. As an engineer I can tell you this is rare for mechanical systems and that's why we construct stiffness matrices and calculate eigenvalues and eigenvectors, at least if we don't want bridges to fall down or turbine blades to let go. Pianos and guitars are mechanical systems where the overtones do not have those simple relationships. That adds a complication beyond the difficulties of temperament. (inharmonicity)
My interest is mainly that the better I can learn to listen to subtle differences, the more precisely I can play and maybe sing in tune. Or at least know when I'm wrong.
I don't know much about the voice and its overtones. I've always assumed the overtone relationship must be different because you can sing the same note on different vowels. Something for me to research, I guess. Maybe you've looked into this.
Back on topic, to my ears the overtone singing done at the concert and by Anna-Marie is neither quite ET nor quite a pure interval.
Back off topic, a trombone player I know from forums,who's a working pro in NY, uses overtone singing as a guide to shaping his vocal cavity for expanding the high range. It's intriguing.