This is mad.
Two women face each other, usually holding each other's arms. One singer leads by setting a short rhythmic pattern, which she repeats leaving brief silent intervals between each repetition. The other singer fills in the gap with another rhythmic pattern. The sounds used include voiced sounds as well as unvoiced ones, both through inhalation or exhalation. The first to run out of breath or be unable to maintain the pace of the other singer or the first to laugh, or to simply stop, will lose the game.
At one time, the lips of the two women almost touched, so that one singer used the mouth cavity of the other as a resonator, but this is less common in present day. Often, the singing is accompanied by a shuffling in rhythm from one foot to the other. The sounds may be actual words or nonsense syllables or created during exhalation.
That first video is a pleasant example of this Overtone technique, though I have found that so much online footage is teaming with background noise and instruments, and right now the main thing I am interested in is the actual singing itself.
What is happening there is that the partials (fundamental and overtones) of a sound wave made by the voice are being selectively amplified by changing the shape of the resonant cavities of the mouth, larynx and pharynx.
This resonant tuning allows the singer to create apparently more than one pitch at the same time (the fundamental and a selected overtone), while in effect still generating a single fundamental frequency with his vocal folds.
The below video is from the Chevy Chase show, so forgive the mid 90's wholehearted American-ness of it.
That said, with no background distractions or hullabaloo, this is one of the best pieces of documentation I have found showing off Overtone throat singing, and I am pretty certain it will blow your mind.