My guess would be that you’ve only stored some of the internal project files on Dropbox—either that or you’ve only chosen to download parts of the project. A project is the entire folder ending in “.scriv” and everything within it. Copying any less than the entirety of that folder will not be a complete project.
Incidentally, it’s a lot easier to install Dropbox on both PCs. They will handle all of this uploading and downloading for you automatically, as you work even. No worries if you can’t do that—I know there are many places that don’t let you install it, or maybe you just don’t want to. It’s okay to use the website, but you will need to take care to transfer the whole project. A good tactic is to .zip archive the project before uploading it. This will transfer much faster, and there will be no ambiguity over whether you’ve downloaded the whole thing since there is only one file to worry about.