Google Drive does export sub-folders, but only when they have content.
Simply find the folder you want to export in the left-hand sidebar, click the down arrow next to it, and select Download:
There is a 2GB limit, so if the sum of filesizes in your folder tree exceeds that, you may run into trouble.
If that is a problem, another solution is to set up synchronization with your computer. Then you'll have a copy of the entire Google Drive on your hard drive, and you are free to create a zip file from any folder you'd like, from your computer.
See Overview of Google Drive for help installing the Google Drive client on your computer.