Ramer's was a manufacturer of chocolate confections. In all our years of researching baseball games, we've never seen hide nor hair
nor even any mention of a tabletop game or handheld game associated with Ramer's, although one of the many "5 cents a play"
punchboard-type gambling games that don't name a specific product or manufacturer is certainly a possibility.
It might also be possible that the candy bar itself was actually named "Baseball Game," just so they could use the tag-line
"Everybody enjoys a Baseball Game."
We've seen an example of this wooden crate before; the text that's been torn off the label inside the lid of your case reads:
Ramer's BASEBALL GAME
40 Bars in this box are FREE
for advertising.
Here's a current auction for a Ramer's candy box:
http://www.liveauctioneers.com/item/7014946
and here are two old ones:
http://bid.showtimeauctions.com/Rame...Sign_i11127956
http://www.ebay.com/itm/c1920s-Ramer...p2047675.l2557