You're right in that the theatrical bar fights are a lot less likely to happen in the real world. However, this is not to say that bars were not frequently the setting of violent altercations, but there was some method behind it. People weren't stupid, and they didn't often fight for fun. In most cases, there were reasons behind the violence, usually a grudge, a business or legal dispute, or a past insult. Add into this the fact that during the 19th century, Americans consumed about three times as much alcohol per capita as they do today. If you've got a drunk in a bar, nursing his resentment with 100-proof whiskey, and an enemy walks in, maybe they exchange harsh words. Maybe it escalates to exchanging blows, or, if one or both is armed, they spontaneously pull firearms and go to shooting.

If we look at, for instance, the famous "Four Dead in Five Seconds" gunfight, which occurred in El Paso, Texas in 1881, we see a classic example of drunken, impulsive, and deeply personal violence. A cross-border rustler by name of John Hale had killed two Mexican ranch hands sent to investigate the theft. An El Paso constable, Gus Krempkau, found the bodies and testified against Hale in court. Later, Hale and a friend, George Campbell, encountered Krempkau in the street. Both Hale and Campbell were very drunk, and evidently fell into dispute with the constable. Hale, who was unarmed, took one of his friend's pistols and shot Krempkau. The town marshal, a dubious character named Dallas Stoudenmire, had been eating across the street, and came running. His first shot killed a bystander; his second hit Hale in the head. Campbell attempted to surrender, saying "Gentlemen, this is not my fight." The mortally wounded Krempkau then shot him through the wrist, and Stoudenmire, for good measure, emptied his pistol into Campbell's stomach.