Tom Mix is "Texas", a cowboy on a ranch. He tracks the man who left his sister to die in Montana and shoots him. Then second episode: Texas and the sheriff are love rivals for Moya's hand, until Texas arrests Franck after robbing the stage. Third episode: Texas is now the sheriff, and arrests Moya's former foreman as he rustles horses and kidnaps Moya.
This structure in episodes in itself is troubling; at 42 minutes the whole film is way too long, since the episodes have now link together. It looks like the "editor" -- and Selig -- were looking for a way to have a 4-reeler while actually shooting one-reelers. You have the three episodes spliced together, three for the price of one. Is this an influence of "The Perils of Pauline" ? Moya looks a little like helpless Pauline, always getting caught up in the villain's schemes, unable to do anything about it, except maybe force the good guy to come to the rescue double-quick.
Long shots, no close-ups, rudimentary editing, linear, following the plot in the most thorough fashion. Although the actors, lit by natural light, their faces dark under their hats, are hard to read and recognize (see other comments), the film follows them, and shows its overiding interest in the figure of the cowboy. There is no attempt to place them in their geographic context, no attempt to describe anything but the different types of cowboys you can find out West: the hand on the ranch, the proud, quick-on-the-draw, honest Texas, the cowardly sheriff... It's obvious that here this western is still trying to bank on the popular image of the cowboy as dime novels would have created and distributed it; the cowboy, and not the West. Later westerns will focus more on the land, less on the myth of the cowboy. But here, we are still in that tradition. So what really matters for the audience is to know what a cowboy would do in such and such circumstance: in the first episode, tracking the villain is of no interest to the film (we cut from Texas leaving his ranch to his getting to Montana, and then he finds the man by chance). What is interesting is what Texas, the perfect type of the perfect cowboy, will do when he finds him: the shoot-out, his heroism, his honesty, his markmanship. The audience wants to see a romantic cowboy, and that's exactly what it gets.
Tom Mix here uses his mournful, pathetic vocabulary of pantomime (as opposed to the burlesque of "Bear of A Story", for instance), with no stunt to speak of (except getting on and off a horse in a very sleek way). He sighs, cries, and is even mortally wounded (he looks like he's about to die until the next shot, where he is alive and kissing Moya).
A note on the interior shots in the saloon (apart from a shot inside the post office -- what other western has a practical post office, anyone knows ?-- all interiors are of the saloon): cramped, door to left, bar in back, a table in front. Usually the cowboys are standing at the bar. Like in Hart's "Return of Draw Egan", the bad guys are not sitting at the table doing nothing or playing a listless game of poker. They stand at the bar, and only sit when they actually have to actively plot something together (contrast this with the bad guys in "Shane" who spend all their time doing nothing sitting at a table in the bar, and no one is standing at the bar: that's the history of Hollywood style, folks). THe reason is here visual: by standing at the bar they have their backs turned to us, thus looking more ominous, hard to fathom, than if we could see their faces (cf. the shot of the Mexican villain's back, his ornate jacket, before we "see" his darkened face).