While this house design falls into the category of Contemporary Southwest Architecture, it borrows from historical Native American and Hispanic structures build in the high desert regions of the South West. Those historic structures were instinctively natural in fit and function. Of course we live somewhat differently these days, so this design responds to sustain 21st century living, with gratitude for the lessons learned from our predecessors. Our predecessors did not try to compete with the beauty of the land, but rather to fit in gently.
A word about "Contemporary". The origin of the word is from the mid 17th century: from medieval Latin contemporarius, from con- 'together with' + tempus, tempor- 'time'. I like to think of it as "the current tempo" which is always changing! This is different from "Modern" which implies a departure from traditional styles and values. Here is a broadly accepted definition for the adjective "Contemporary":