Learn Polish: Nie mam czasu na oglądanie telewizji. - I do not have time for watching television.

Oglądanie is a verbal noun meaning "watching". It is formed from the imperfective verb oglądać (to watch). To make it, you simply drop the final -ć from the infinitive and add the suffix -nie. It then functions exactly like a standard neuter noun.

Since we say "oglądać telewizję" (Accusative), why does this sentence use telewizji (Genitive)?

This is a very important rule for this lesson! While verbs take their usual objects (like Accusative), verbal nouns act like regular nouns. In Polish, when a noun describes another noun, it takes the Genitive case. Literally, you are saying "the watching of television". Therefore, telewizja changes to its Genitive form, telewizji.

Why doesn't the negative nie mam change oglądanie into the Genitive case too?

The negation rule (changing an Accusative object to Genitive) only applies to the direct object of the negated verb, which in this case is czasu. The word oglądanie belongs to the preposition na (meaning "for" a purpose or activity). The preposition na always dictates its own case—here, the Accusative—regardless of the negation earlier in the sentence. Because oglądanie is a neuter noun, its Accusative form is identical to its Nominative form.

Just as a refresher, why is the word for time spelled czasu here instead of czas?