http://www.dictionary.com/browse/steampunk:
steampunk
or steam punk, steam-punk
[steem-puhngk]
noun
a subgenre of science fiction and fantasy featuring advanced machines and other technology based on steam power of the 19th century and taking place in a recognizable historical period or a fantasy world.
https://en.wikipedia.org/wiki/Steampunk:
Steampunk is a
subgenre of science fiction or science fantasy that incorporates technology and aesthetic designs inspired by 19th-century industrial steam-powered machinery. Although its literary origins are sometimes associated with the cyberpunk genre, steampunk works are often set in an
alternative history of the 19th century's British Victorian era or American "Wild West", in a future during which steam power has maintained mainstream usage, or in a fantasy world that similarly employs steam power.
So, no, definitely not steampunk by definition.
1. Steampunk is scifi / fantasy.
2. Steampunk is
alternative history. Westerns are set in the
actual world of the 19th (or 20th!) century. They take the history of the American West as it actually was.