This is entertaining but its ending falls flat. I like the banter between the man and the characters. I like the Man, he's cool and tough. You've portrayed him well. I liked the scene with the poker players getting what they deserve.
"An openly gay sheriff in the old west must endure a shocked town folk, a corrupt Mayor and a wealthy land baron intent on ridding himself of the newly elected sheriff."
Unfortunately your logline is way off.... we don't see any shocked town folk, the 2 people that do find out he's gay are okay with it. The corrupt mayor? not a huge indication he's corrupt, and who is the wealthy land baron intent on ridding himself of the Man?
It just needs a good ending, at the moment it's about a guy who comes to town, shows a bunch of assholes a thing or to, comes out to the waitress, gets noticed by the major, offered a job, offers the guy he has an attraction to a job, he takes it and thats it...
You've done a good job with the character, just need to build on the story.....
Keep at it!