To have an direct access of a file on Dropbox, you have to replace the shared link's subdomain www with dl. The main domain gets redirected from dropbox to dropboxusercontent.
I wonder how (if possible) to host a static single page website with external CSS and image files. These external files are in sibling directories, but the html file doesn't seem "to be aware" about these.
This isn't possible with a share link, since relative paths don't work. (Each path has its own signature in the URL.)
However, you can do this with a public folder, or you can use third-party hosting. I'll refrain from plugging my startup here, but there are a number of good options. :-)