The museum has a number of real, restored aircraft, and a number of replicas. The website is incomplete with regard to the museum's collection and sometimes even the signage doesn't make it clear which ones are which.
However I have a strong suspicion that this BE 2 is one of the latter if only because there are depressingly few genuine World War I fighter aircraft left around.
Especially BE 2's which, while a very good aircraft for its time, was an absolutely appalling fighting machine susceptible to being knocked out of the sky if a Fokker so much as gave it a filthy look. Nonetheless, this display is realistic enough that you can almost imagine yourself up there, feeling the bugs grinding against your teeth.