This is obviously hilarious, but I also find it extremely touching, and I've spent a few days trying to figure out why.
I think it has to do with the childlike simplicity/purity of the narrative she's constructing, plus her absolute commitment to it...and the beauty of the participants contagiously, inexorably coming to buy into it* as well. If only human sociality could be thus.
But there's a deeper facet. What Conti's doing here could be seen as horribly fascistic. It could easily seem terrible! But her utter benevolence - and great sensitivity (it's more Conti empathically observing and accounting for the woman's micro-behavior than the woman tailoring her behavior to Conti's narrative) is deeply generous and touching. Someone in a position of profound dominance and advantage choosing sweet sensitivity and generosity reads as a pure (and rare) expression of the better angels of our nature.
The children's book "The Witch Next Door" shows the exact same thing, and it's the most touching book I know.
Finally, something about a strikingly beautiful woman and studly guy donning grotesque masks and struggling to present themselves and to connect with each other - and, thanks to the ventriloquist's angelic deus ex machina, making it work in a sweet, childlike way - strikes a chord. The widespread acceptance of the "hot guy"/"hot chick" meme as apotheosis-of-love strikes me as sad, but Conti has subverted that narrative to create a cartoon which, at a visceral level, somehow strikes at the more pure-hearted essence of how romantics like me prefer to view love. The audience's recognition of the flagrant and clumsy manipulation required to bring it about lies at the root of the power and bittersweet beauty of the piece.
* - I mentioned "the beauty of the participants contagiously, inexorably coming to buy into it". That very progression looks, quite strangely, something like the process of actually falling in love. As the participants buy into the shtick, in other words, and yield more and more to the narrative, Conti has contrived to model something truthful about actual love. (Her talent for cajoling truth must make her a hell of a film director; I'm looking forward to viewing her film, linked below!)
Nina Conti's web site
Conti's film: "Her Master's Voice"
A couple of performance videos, available at UK Amazon: "Nina Conti - Dolly Mixtures" and "Nina Conti - Live - Talk to The Hand"
A review of "Family Tree", Christopher Guest's short-lived but apparently quite good HBO series featuring Conti.