Love that song, and love Marty Robbins in general.
It is of course pedantry, but technically I'd classify that song as "western" rather than "country." They have distinct sounds, and although you could argue that western is a subgenre of country, I'd reply that there's a reason the whole deal is referred to as "Country and Western" music.
And "El Paso" is pretty much the archetype for a western epic storytelling ballad.
