Hi Scott,
I'm not 100% sure, but I believe there is a possibility that the coupon you are asking about could have been used for promotions that included a free Coke (pop) or some other concession. Other teams did this- the Cleveland Indians comes to mind.
I will tell you that it is from circa 1950's based on the Red Sox logo font used on the front of the coupon. BTW, I have BoSox tickets (G/A and bleacher stubs) from this era that have the same font and the ticket stock/color appears to be nearly identical FWIW.
I hope this helps! I look forward to what other responses come back from other members that have Red Sox local knowledge.
Good luck!