I am almost sure it was Gunfight.
I was playing this always with some friends on my Atari 65XE when I was young.
I checked and it was released to Atari 2600 as a cartridge too.
Just search for some Atari Emulators and Gunfight for Atari.
BTW Gunfight for Atari800XL/65XE has better graphics as I compared movie from 2600 version to my memories.