As to why I think the game was so significant, I'll just quote something I wrote years ago at the old blog:
I honestly never get tired of reading about this game. It's significance really can not be overstated. The Brown Stockings victory over Chicago on May 6, 1875 did several things that helped lay the foundation for St. Louis as a "baseball city."
First, it united the city in a way that it had never have been united previously. Between the heavy influx of German and Irish immigrants, the political divisions brought about by the Civil War, and the natural conflict between the Creole founders of the city and the Americans who moved to the city after the Louisiana Purchase, St. Louis was a city divided along economic, political, and racial lines. The Brown Stockings' victory on May 6, however, was embraced by almost the entire populace of the city. No other event and certainly no other baseball club had ever seen the fervent outpouring of support that the Brown Stockings received in 1875. While it's now common to see the city united by its love for her baseball team, this was the first time it had happened.
Secondly, this game cemented the St. Louis/Chicago baseball rivalry and placed the two cities, baseball-wise, on an equal footing. One of the reasons for the joyous celebrations that erupted following the game was because of the overwhelming dominance of the Chicago professionals over the St. Louis amateurs in years leading up to 1875. This game proved that St. Louis would no longer be a push-over for its northern neighbors and chief economic rival.
Finally, the game marked the end of the pioneer, amateur era of baseball in St. Louis and it's successful debut in national, professional competition. No longer would clubs such as the Empires or the Union hold a place of prominence on the St. Louis baseball scene. The new focus would be on the professional clubs who would attempt to bring in the best players they could afford. There would certainly be struggles in the years ahead but after May 6, 1875 there was no turning back.