But overall, romantic comedies and action movies I like.
Grammatically, this is called preposing, which occurs when some element is put before the subject of the clause when its basic position would be after the verb. In this case, the object of "like" ("romantic comedies and action movies") has been preposed.
Semantically, the preposed element is not used for emphasis, but to serve as a link to the preceding discourse: if you listen to the earlier part of the video, you'll notice that the speaker was talking about action and adventure movies, and romantic comedies, so the preposed element ties in with the things he was saying earlier.