Who was the first philosopher to write seriously on the topic of movies, cinema, video games and other modern artifacts of popular culture?
Is there a good reference covering the birth of this branch of philosophy (critical theory?)
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Critical theory, focused among other things on popular culture, dates I should say from the Frankfurt School founded in 1923 at the Institut fur Sozialforschung. There are no abrupt beginnings in the history of social theory; prefigurations of the work of the Frankfurt School are evident in Georg Simmel or even earlier in (how can we avoid the name ?) Marx.
Early members of the Frankfurt School included Carl Grunberg, Max Horkheimer. Friedrich Pollock, Leo Lowenthal, Theodor Adorno, Herbert Marcuse, and Erich Fromm formed an inner circle around Horkheimer, who became Director in 1930. It was in the 1930s and 40s that the School started to pay serious, systematic attention to the Nazi penetration of German society, to aesthetics, and to popular culture.
The School's influence greatly expanded when under Nazi hostility it relocated to Holland in 1931 and, of crucial importance, when in 1934 it re-established itself as the 'Institute of Social Research' at Columbia University in New York. The transatlantic transfer transformed the School into a formidably influential intellectual force.
A useful source is Martin Jay, The Dialectical Imagination. Boston: Little, Brown and Company, 1973.
Since there was so much collaborative work in the School, it is perhaps invidious to name the first philosopher who undertook the type of social analysis you are interested in. But Horkheimer's inaugural lecture as Director, 'The Present Situation of Social Philosophy and the Tasks of an Institute for Social Research', puts popular culture clearly in its sights. See Max Horkheimer, 'Between Philosophy and Social Science: Selected Early Writings', tr. Frederick Hunter, Matthew S. Kramer, John Torpey, Cambridge: MIT Press, 1993.
This answer mainly collects suggestions given in the comments section: