I found this article in the December 25, 1875 issue of the St. Louis Globe-Democrat and have been sitting on it for about a year. The problem is that I don't know for sure if the Christmas game between the Brown Stockings and the Empires ever came off. I'd like to believe that there was a baseball game in St. Louis on Christmas Day 1875 but I haven't been able to confirm it.
Charlton's Baseball Chronology does have this entry for December 25, 1862:
At Hilton Head‚ SC‚ a baseball game is played between teams selected from the 165th New York Volunteer Infantry‚ Duryea Zouaves. The match draws a crowd of 40‚000 soldiers and is the talk of the military world for weeks after.