The state, condition, or rank of being a dilettante; superficial engagement in an activity or field of study.
From dilettante plus the -ship suffix, which denotes a state of being or social position (as in 'friendship' or 'leadership'). The suffix comes from Old English and creates abstract nouns.
The -ship suffix historically marked rank or membership—think 'membership,' 'citizenship,' 'kinship'—so 'dilettanteship' is like saying 'the club of people who dabble!' It's a witty way to critique casual engagement.
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