I think what confuses you here is seeing the dative case as simply meaning indirect object.
In Proto-Indo-European (PIE, the theoretical language which all European languages evolved from) there were eight cases, including the four which remain in modern German; one of the others was the locative case, used for marking the location where something takes place. Very early on in the development of the Germanic languages out of PIE, the locative case was effectively merged with the dative case, meaning the dative case took on some of the locative case's functions.
In Slavic languages like Russian and Polish, which also evolved out of PIE, the locative case (or equivalent) still exists independently of the dative case, and is used in contrast with the accusative in constructions similar to the examples given in German to distinguish action in a place from action towards a place:
Russian – Polish – Meaning:
Я иду в парк. – Ja idę w park. – I walk to the park. (парк/park is in the accusative case)
Я иду в парке. – Ja idę w parku. – I walk in the park. (парке/parku is in the locative case*)
(* парке is actually in the "prepositional" case, which is the Russian equivalent of the locative)
In German, expressions are formed with exactly the same structure, but because the locative no longer exists, the dative is used instead:
German – Meaning:
Ich gehe in den Park. – I walk to the park. (den Park is in the accusative case)
Ich gehe in dem Park. – I walk in the park. (dem Park is in the dative case)
The dative case is not being used to indicate an indirect object here; it is merely filling in for the now deceased locative case. As the sentence in your question is concerned with the location of the action (sitting) rather than the target/direction, you would use the dative, which performs the function of the locative after the preposition in:
In dem Kino sitzen Bürger.
Remember: Linguistics attempts to generalise about languages, and defines categories that are roughly equivalent across different languages; but every language has evolved its own unique conventions and idioms, which don’t always exactly match up with those of other languages or general linguistic categories. An understanding of general linguistic concepts is certainly very helpful when learning languages, but one should remember that every language is different and expect to encounter idiosyncratic structures or usages or expressions which seem erroneous when compared to generalised definitions of concepts. Every language has its own whimsical little rules that aren’t always straightforward to analyse, and just have to be learned.