Actually, Haus des Geldes and La casa de papel are not equivalent. @HubertSchölnmast and @Urgard correctly described what the phrases mean in their respective languages, but what matters most here are the differences between how Romance languages and German express compositions of nouns. I'll try to unravel the hidden misunderstandings first and explain the difference.
The key is what you wrote in the question:
La casa de papel gives an idea of papel [belonging] to the casa …
That corresponds with @Urgard's statement:
When I read La Casa de Papel, I see in my mind a house MADE OUT of paper
That is because at least in French, Italian and Spanish (probably also in Portugese and Romanian), the simple de/di without article does not correspond to the German genitive, but would be substituted in German by a compound noun:
- La casa de papel
- La maison de papier
- La casa di carta
- Das Papierhaus
I guess this is what you meant with "papel belongs to the casa" and insofar you are right. @Urgard almost said this; however, it's either Papierhaus (literal) or Geldhaus (metaphorical), not Goldhaus (that would be casa de oro).
So it's important to note that casa de papel in fact means house of paper/paper house and would be called Papierhaus in German, but another title was chosen in German that is not a translation of the original title as you can see here which I will explain further below.
Different from that is the genitive. That would in all languages require an article:
- La casa del papel
- La maison du papier
- La casa della carta
- Das Haus des Papier(e)s (or: Geldes)
If you have a phrase like that, it indeed means that the house 'belongs' to the paper (not the other way round). But interestingly, in German this can also mean the house is dedicated to paper, or, more applicable here, money, like a bank or a money printing office.