"Gazete okuruz", means: we read newspaper. You are correct (literally)
Gazete is, the indefinite, direct object. Duo accepts both singular & plural forms in English.
You can add (a) & the plural suffix (s) to the English answer. Both are correct. Please see my answer above.
Turkish grammar rule:
The indefinite, direct object (gazete) in the nominative case always goes immediately before the verb.