Recently someone posted a link to Caraveneer[1], which is very much tiled graphical when it comes to combat (rogue-like, if multiple player-controlled characters are your thing) and was addictive enough for me[2] to leave me doing little else for far too long. And there's plot-line issues to deal with, as you can't just keep going round the obvious circuit indefinitely due to supply and demand being affected by your own actions[3].
Not quite Wild West, as it's supposed to be a post-apocalyptic (well, global-warming) future with "Mad Max-lite" travel options (once you get to where there's vehicles), but it's really not too far from pure horses'n'gunsmoke era if you stick to the vehicle-less areas and treat the M16s and rocket-launchers that you can still buy there as being just mildly anachronistic for the otherwise Wild West setting...
[1] Easy to search for in Google, first link is a good in-browser playing link, but the second one down is the SugarFreeGames page (the developers/publishers) with a full download of the game, then there's the SFG "Play in browser" one, IIRC. But the downloadable one will probably let you save your progress (without creating accounts on the appropriate online provider's site) rather than have you sitting at your machine for eight or ten hours straight.
[2] I have the spreadsheets and text notes to prove it!
[3] On the other hand, after the hundredth time seven guys with swords try to attack your three gun-men and fail, you begin to wonder why they aren't running the other way when they see you coming, instead. But "getting attacked by robbers with horses" (who seem to be surprised to be attacking you) is a good way of getting additional fodder, if you also resist the temptation to take the horses and carts themselves meaning you're almost as low on fodder as you were. I imagine the same will happen with more advanced vehicles, but I decided to rip myself away from the game before that happened.