Not only is Wyoming solidly in the west, Wyoming arguably defines the west. Cowboys, sagebrush, the Rockies... If any part of Wyoming is "the midwest," so is the moon.
The truth is that pretty much everything about the western US starts with California and then spreads back out. This is because, due to the gold rush, California was settled and made a state first, while the rest of the western states remained "territories" and only achieved statehood much later as they too became more heavily settled.
Basically, the settlement pattern of the western states is backwards after about 1852 or thereabouts, with the California and the west coast filling in first, and the interior states filling in later.
According to google the town of Midwest, WY has 283 people, which is damn near half of the state's population. So add in a few more confused cowboys and that checks out.