The sentence you wrote is perfectly correct. Yes, the verb gostar is always followed by a preposition (de, da, do, das, dos). Gostar isn't always followed by de, it all depends on the genre of the word that the verb refers to. DE used with the verb gostar: it is used when we talk about something that we like in general, for instance, I like books/Eu gosto de livros, in this case I didn't say whose books I like or what kind of books I enjoy reading. e.g: Eu gosto DE ler muitos livros/I like reading many books. e.g:Eu gostei DO seu vestido(masculine word)/I liked your dress. e.g:Eu gosto DA cor(feminine word) dos seus olhos/I like the color of your eyes. e.g:Eu gosto DAS músicas(Plural feminine word) da banda Linkin Park/I like Linkin Park's songs. e.g:Eu gosto DOS quadros(Plural masculine word) do Picasso/I like Picasso's paintings.

The sentence is correct. Subject:: a duração dos vídeos Linking verb: foi Adverb + Action verb + Preposition: mais gostei de direct object: o que eu In a normal sentence, the subject comes before the verb, while the objects come after. Only happen contractions (de+o(s)/a(s)) when the preposition of action verb is used before the article. This just happened once because there is only one preposition.

Olá Justin, ficaria: A frase perfeita e correta (ou no diminutivo - corretinha) seria: "O que eu mais gostei foi a duração dos vídeos" Talking about daily portuguese, this phrase above sounds better but the phrase that you wrote with "da duração" is also right.