I think that I've made a decent argument for the game's significance before, mentioning that the victory unified the city behind one baseball team for the first time, that it cemented the St. Louis/Chicago baseball rivalry, and that it marked the end of the pioneer era and the beginning of the professional era. But there is one more point I'd like to make about the significance of the game, relating to the last point.
There was no reason that professional baseball had to succeed in St. Louis. There was no reason that St. Louis had to become a "baseball town" and develop a deep-rooted love of major league, professional baseball. These things were not preordained. They did not have to happen. But they did. And I would argue that one of the major reasons these things did happen was because of the Brown Stockings' victory on May 6, 1875.
This victory legitimized the Brown Stockings. It legitimized the decision to bring in the best baseball players the club could sign. It legitimized openly professional baseball in St. Louis. I don't think too many people appreciate the fact that this was a risky venture. It was something that had never been tried in St. Louis before and there was a significant chance that the club would fail (as it eventually did). The Reds were sitting there, with a club made up of local talent, hoping the Brown Stockings failed and ready to reap the reward of that failure. The Empire Club was sitting there, stuck in the past, hoping the Brown Stockings failed so that things would go back to the way they had been.
But the Brown Stocking model - borrowed from the Eastern clubs - worked and brought winning, professional, championship-level baseball to St. Louis for the first time. While the game and the business of baseball has changed substantially since 1875, that model still works. It's been used, in St. Louis, by Chris Von der Ahe and the Robisons and Sam Breadon and Gussie Busch and Bill DeWitt. The model has been heavily modified but the idea of purchasing the best baseball players you can find and putting a club together to compete for the national championship still stands and still works.
Men like J.B.C. Lucas, Orrick Bishop, W.C. Steigers, Mase Graffin and those involved in putting together and managing the Brown Stockings essentially created modern baseball in St. Louis. Asa Smith tried to do this a decade earlier but, while he had a great deal of success in modernizing St. Louis baseball, he failed to put together a club that could compete nationally. The brain-trust behind the Brown Stockings, while they failed to win a national championship, was able to put together a championship-caliber club that could compete with the best clubs in the country.
The victory over Chicago was the earliest proof of that. And, as I said, it legitimized the Brown Stockings and their business model. The way the Brown Stockings went about creating their club was different than the way any other St. Louis club had ever gone about putting a club together. Their success established openly professional baseball in St. Louis and helped establish St. Louis as one of the great baseball markets in the country. If the club had failed and if they had specifically failed against Chicago, it's possible that none of that would have happened.
There would be ups and downs along the way - the collapse of the Brown Stockings, Von der Ahe's struggles in the 1890s, etc. - but after May 6, 1875 there was no looking back. The pioneer era was dead and buried in St. Louis. A new professional era had begun and the city was on the path to becoming one of the great baseball markets in the United States. As a historian, a baseball fan and a St. Louisan, I find that significant.
Plus, you know, it's always good to beat Chicago.