Should it be reopened?
I don't think that it is an off-topic game identification question. It's not the "I remember this thing about a game, what game was it"? type of game identification question that we close as off-topic here. I believe the close reason was used incorrectly. It's more similar to other on-topic gaming-history questions on this site.
As for the question asking for a list or its topic broadness, I think a question should be closed for that reason only if it is asking for an unbounded or open-ended list, or a very large list of items, which is not the case for this specific question. According to Arqade's site tour, one shouldn't ask about:
Questions with too many possible answers or that would require an extremely long answer
I don't think the question fits that criteria. Several positively-received gaming-history questions actually have multiple games in the answers.
Related meta post about a similar list-type question where the community voted to reopen: Why was my question about games in a compilation closed?
Also, I concur with @pppery's comment regarding moderator actions on a disputed question:
Also note the question was closed by a moderator acting doubly (meaning it would have taken two community members without diamonds to close the question) despite having passed the close vote queue, and then left closed again by the same moderator acting doubly. This sort of question is not the right time for moderators to use their moderator powers. [...]