"das geht leider nicht" - which noun is the "das" here an Artikel for?

In this sentence, das is not an article, but a demonstrative pronoun (Demonstrativpronomen). It refers to the verbal phrase ins Kino gehen.

While diese[r,s] ('this') and jene[r,s] ('that') usually refer to real things and are somewhat emphasizing, der/die/das often refer to things from speech and are less emphasizing. There is no complete English equivalent, however it matches closely French cela/ça and Italian ciò, for example.

Der and die can also be used as demonstrative pronouns for nouns with the respective gender. Verbal phrases, however, are always refered to by neuter das.

does not have any nouns

Such sentence never appears out of context (usually a question, but not necessarily).

so what is the das for?

Das refers to the verb and noun introduced in the question before (in[da]s Kino gehen).

It's merely the same as in English you say:

Would you want to go to the cinema with me at saturday?

That's unfortunately not possible.

Check @amadeusamadeus answer for the exact grammatical definition (Demonstrativpronomen).