According to the Historic American Buildings Survey, the Cleveland Avenue Gatehouse was the last building constructed by Henry Shaw, completing his vision for his botanical garden.
And how the world had changed. When he first had arrived in St. Louis, the United States was far different; Shaw could and did own slaves, and was able to retire in middle age because he had grown so wealthy. By the time he died, the Civil War was decades behind him, and architectural styles had changed dramatically.
Classical revival styles had fallen out of favor (but would soon see a resurgence) and the picturesque style of the Romanesque Revival, as this building was designed, were in vogue.
I looked at this house long ago, back in May of 2013.