A Term for Someone Who Constantly Quotes Film/Literature/Poetry

If they are using direct quotes, they may be a quotationist:

A person who habitually uses quotations

Despite sounding mildly made-up, the Oxford Living Dictionary notes that it is a term from the field of Literary Criticism first used by Milton in the 17th century.

An allusionist is someone who habitually uses allusion, which is an implied or indirect reference. So this better describes someone e.g. using or paraphrasing quotes to reference something about their original context rather than someone referencing them by the name of the work.

And of course, given the audial similarity to illusionist, it will be less likely to cause confusion when written rather than spoken. Such, I suppose, is the power of the illusionist, to make things appear other than as they are.

How about Quoteman ? It would be nice near hundreds words with termination man,like statesman,ashman,barman,spokesman,postman.

Maybe you could call them a “sampler”? Like Baby from Baby Driver using quotes from movies and previous statements from others throughout the movie

How about a Connoisseur? ...a person who has a great deal of knowledge about the fine arts, cuisines, or an expert judge in matters of taste.

The definition doesn't implies that he goes around quoting stuff but IF you are a connoisseur then you might quote from time to time to exercise knowledge or superiority.

Connoisseur according to wikipedia.