Most of the mentions of gambling from the 1870s and 1880s that I've run across pertain to Joplin and Baxter Springs, but I'm sure other towns, at least those of any size, like Springfield, also had their fair share of gambling establishments. By far the most popular game at the gambling houses was faro, but many of them also offered poker, keno, and other gambling games. Faro is no longer played in most casinos, because, unless it's a crooked game, the odds don't favor the house enough to justify it.
Men from the 1870s and 1880s, though, didn't have to go to gaming houses to gamble. They would bet on virtually anything: foot races, horse races, prize fights--you name it. Horse racing was probably the biggest competition for betting (outside of the gambling houses), but I imagine they even bet on baseball games.
By the way I have also been struck by how popular baseball was even as early as the 1870s and 1880s. It was not unusual for teams from neighboring towns to play each other. Often they were not affilated with schools as they almost always are today but instead were called "town teams" and were composed of any young men who wanted to play and could help the team. During this time period, basketball had not yet been invented, and the rules of football had not yet been standardized. The game still more closely resembled rugby than the game we know today as American football. So, I guess the popularity of baseball should come as no surprise. After all, that's why it has traditionally been known as the American pastime.