The root word of "angst" is Ang, as in Ang Lee, master of angst-ridden cinema. He did suburban angst in The Ice Storm (1997). He gave us the angstiest Hulk in the form of Eric Bana in 2003. And why do you think the tiger is crouching and the dragon is hidden? Angst.
So Lee was the perfect fit for a film about tortured gay cowboys. But he wasn't the first choice. Gus van Sant, director of another gay cowboy film called Good Will Hunting, was attached for a while.
After reading Proulx's short story, Lee loved it, practically saying "I wish I knew how to quit you" to the printed page. Lee's determination was rewarded with an Academy Award for Best Director, making him the first person of Asian descent to win the award. He would repeat the achievement later with Life of Pi (2013), going from saying "howdy, tiger" to a couple of a rough-and-tumble cowboys to saying "howdy, tiger" to an actual (CG) tiger. (Source)