I am looking at the following demo - http://blueimp.github.com/jQuery-File-Upload/
To my understanding in the demo, php files are being served from github which mean
No, you can’t.
Github Pages let you serve web client content (HTML, Javascript, CSS) without the need of owning and maintaining a web server. You can make sub folders, map your domain into it. Use tools such as Jekyll or Hugo with some basic programming skills, you can make your site work as good as an CMS.
However, it does not allow you to use any backend technology to process and manipulate data/logic.
So, PHP is not possible.
Github Pages is not a full-featured web host. It will not execute PHP, or any other arbitrary code.