Because I live under a rock, I saw this video for the first time only recently.
First of all, gendered muppets. Physically, Mahna Mahna is gendered masculine, with a low, gravelly voice and masculine dress. The Snowths are gendered feminine; they're pink and have exaggerated eyelashes. Let's just pause for a moment to register how odd and not-odd it is to gender muppets. Insofar as they are anthropomorphized and people are preceded by gender, it is not surprising that muppets are gendered. But given how far the producers go out of their way to make them nonhuman, the degree to which they are gendered is surprising.
Even more surprising is how well the muppets' physical gendering harmonizes with the gendering of the actions that they are made to undertake in this video. Supposedly the muppets are just singing a song, but in the process they stage a drama of creativity and regulation that echoes Victorian gender stereotypes.
Muppets are by definition mechanical; they're puppets manipulated by artists from below, and this song is more mechanical than most; syllables, "words," and phrases are repeated over and over. But within the framework of that mechanicity, Mahna Mahna keeps attempting to improvise solos or otherwise depart from the repeated chorus. The Snowths -- two entities acting not as individuals but as a (female) class -- seem to have stepped out of Desire and Domestic Fiction; they survey Mahna Mahna and, with their gaze -- first wondering, then disapproving -- constrain him within the bounds of the repetitive, mechanical chorus. They are not violent; they are not coercive; they simply shake their heads. Influence is all.
Shrinking before them, Mahna Mahna curbs his desire to deviate from the mechanical pattern in which the Snowths, moving synchronously, seem to delight. Like the Widow Douglas trying to "sivilize" Huck Finn, the Snowths set and enforce rules, unable to understand Mahna Mahna's masculine creativity and his capacity for play. The Snowths are didactic Maria Edgeworths to Mahna Mahna's fantasizing George Macdonald; they are petticoat government to a fun-loving Rip van Winkle.
Repressed, Mahna Mahna attempts to escape into the background, turning his back on the Snowths in order to engage in his play. He cannot escape the feminine gaze of social order, however. Even with his back turned, he is aware of the Snowths' disapproval and rushes back to do his manly duty, planting a firm "mahna mahna" between the two bopping Snowths, who continue the chorus in an ecstasy of repetition, as enthusiastic as ever.
Ultimately, Mahna Mahna lights out for the territories -- but he does not forget to call home.
Thus the Snowths' ecstatic repetition of the mechanical chorus, performing the female mechanicity of the "typewriter," the telephone operator, and other modern female cyborgs, returns as technology, only to be shut down thereby. This final utterance of "mahna mahna" puts an end to the repetition that it has so far enabled. Even if Mahna Mahna remains constrained to play house with the Snowths, he can now do it remotely, away from their surveying gaze.
(Far more information than you could possibly want about this song is located here.)