The sentence you have is ambiguous, Mowgli, even with adding the word 'their' in front of 'specific', because 'their' has an indefinite reference--does it refer to humor in the films, or to the people's sense of humor? Also, 'due to' would be better as 'because of'. These constructions are both viable interpretations, although my feeling is that only the first example was the intended one: 1) Because of the specific type of humor in James Bond films, people continue to enjoy them.
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