Pirates serve as a main thematic element, regardless if any pirates are ever seen.
The first video game about Pirate theme was released in 1982.
This requires the pirates are actually a major thematic element instead of just there. For example, Peter Pan has the main antagonist as a pirate, but the story itself is not about pirates or pirate things, thus does not by itself belong here. Though the likelyhood of Peter Pan games focusing on conflicts between the titular character and pirates is extremely likely, pushing them into being pirate themed as well.