"The dining room has a floor."
Translation:Triclinium pavimentum habet.
Not sure what you mean by 'Isn't pavimentum the case?' Pavimentum is accusative singular here (the one being had, the one having the verb action done to).
Triclinium here is the nominative singular form (the doing of the action, the subject, the one doing the having).
Triclinio is either dative (to/for, indirect object, could be used here for a dative of possession with est instead of habet) or ablative (by/with/from, used with many prepositions) singular, neither of which work as the subject.