"Do you want to dance this dance with me?"
Translation:Ĉu vi volas danci tiun ĉi dancon kun mi?
But I thought we only used the accusative N in "tion, tiun, kion etc. when we don't know what the object was. Am I mistaken?
You are probably thinking of the explanation for whether to use tiu or tio. Tio is considered the "don't know what it is" form. Either one takes the -n accusative ending when it is acting as a direct object, as here.