Google drive now supports hosting public webpages, which you can also use to host your games similar to the way people have been using dropbox thus far.
1-Go to your Google Drive (drive.google.com)
2-Press the Upload icon next to "create" in the upper left
3-Choose "Folder" and pick your root of your html5 exported C2 Project
4-When the upload is complete, select your new folder from your drive, and press the little person with a + icon (share) at the top of the page
5-Change "Who has access" from private to public and click Save
6-Copy and paste the big long jumble of letters from the "link to share" field and replace the beginning with this
Note: the index.html at the end.
Now copy and paste that link into a web browser or share it with the world.
Voila. Google drive is now hosting your game.
On a side note: here's an article about how to map a drive letter in windows to your google drive.