True. Even in the example sentence, technically もんか is attaching to the interrogative pronoun なんか, もの is rendering the verb into a noun phrase, and for か to work in the sense of a question it has to be a
sentence-ending particle: "As if I'd be seeing some movie like that, huh?"
A frequent expression you'll see or hear is こんなもんか: "Like this, huh?" As in "All done.", "That's that." or "So
much for that.", "Job done well, if I say so myself." No verb to be found.
I plan to edit this when I get to study this grammar point.
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ものか is a partial match with the grammar point ~など~V-るものか available on page 417 of the Handbook.
Currently, there are three sentences of this on renshuu. The wildcard (*) isn't working in this case for some reason (など*るものか won't work). Search for るものか and then CTRL-F for など.