The original sentence is a shortened version of the this sentence, which just is two full main clauses joined together with und (and) (I put square brackets around each main clause to make them better visible):
[Er hat den Film im Fernsehen verpasst] und [er hat den Film deshalb später in der Mediathek geguckt].
[He has missed the movie on TV] and [therefore he has watched the movie later in the media library].
An even better translation would be: "He missed the movie ..." (without "has") but I need the auxiliary verb "has" for didactical reasons.
The subject er (he) and the auxiliary verb hat (has) can be omitted in the second part of the original sentence, just to make it shorter, giving:
Er hat den Film im Fernsehen verpasst und den Film deshalb später in der Mediathek geguckt.
He has missed the movie on TV and therefore watched the movie later in the media library.
But to avoid repeated words, you can replace one of the appearances of the object with a personal pronoun. But since »der Film« is a masculine noun in German, while »the movie« is neuter in English, this pronoun has to be masculine in German (which gives one of: er, seiner, ihm, ihn) but neuter in English (which gives one of: it, its).
Now you only have to find the correct case, which is easy in English (it can't be genitive case, so the pronoun can't be »its« and so it has to be »it«). In German you must know which case the verb »gucken« (to watch) wants for its object. It wants its object in accusative case, so the pronoun has to stand in this case, and therefore it must be: »ihn«
So, this is the correct translation:
Er hat den Film im Fernsehen verpasst und ihn deshalb später in der Mediathek geguckt.
He has missed the movie on TV and therefore watched it later in the media library.