There was a touch of realism in "jabbing the gun" in the direction of the target. That's simple hip shooting. Frankly, it's a little more realistic than a target shooter's stance and in fact, very similiar stances or positions used to be used in police training. You will often have seen revolver shooters, especially when using single actions, seem to "throw" the revolver at the target. I can attest that it works better than you would expect but it also works better with some revolvers than others. It doesn't seem to work at all with automatics and I expect the radical difference in the grips accounts for that.
With single action revolvers, which in the movies and mostly in real life meant a Single Action Army Colt, you of course have to first cock the gun. At the time a revolver was curiously thought of as a one-handed weapon, so you threw it up and with your thumb on the hammer, cocked it on the way down, the weight of the revolver helping some. On the next shot, the recoil will have the barrel up anyway, so you're in that position naturally. Hammer spurs differ a lot between models but I expect the original SAA form was best for this style of shooting.
You may also notice the gunmen in the old movies moving around a lot, either to make themselves harder to hit or maybe a natural reaction to "dodging bullets." Either way, it's still the movies.