My autism-spectrum son frequently engages in stimming behavior when he is excited by YouTube videos featuring computer games. Wikipedia describes stimming as:
Self-stimulatory behavior, also known as stimming and self-stimulation, is the repetition of physical movements, sounds, or words, or the repetitive movement of objects common in individuals with developmental disabilities and most prevalent in people with autism spectrum disorders. [...] It is considered a protective response to over-stimulation [...].
To me it appears that he is so pleased by what he is watching that he is shaking uncontrollably with excitement. Whereas his stimming behavior used to consist primarily of rocking and arm flapping, it is now frequently supplemented by short bursts of rapid claps.
Wikipedia describes applause as:
Applause (Latin applaudere, to strike upon, clap) is primarily a form of ovation by the act of clapping, or striking the palms of the hands together, in order to create noise. [...] The age of the custom of applauding is uncertain, but it is widespread among human cultures.
I speculate that applause clapping as a learned cultural phenomenon to express pleasure in response to entertainment has its origins in the mimicry of autism-spectrum stimming.