That looks like something that would have been used at the game, like for the public address announcer at the games. If so, that would probably make it pre-1930's. I looked for photos of George Levy who used one at the Polo Grounds in the early years, but came up empty. I did find this but not a great photo.
https://www.publicaddressannouncer.o...-As-Giants.png
Also some live footage, not of NY but will give you an idea of the era.
https://www.youtube.com/watch?v=QGeRFhNlWy4