They are a normal PCB house (or front end for PCB houses). You can send them a .ZIP file containing all the required Gerber files plus the drill file and they should be able to make it, provided the other information is provided by you in the web form.
For example, for a 2 layer board, you would normally send 7 or 8 different files combined into one .zip file (which is a container for losslessly compressed files).
Here is one I have sent off to a different manufacturer. It has an outline file .GM3, but no bottom overlay file. The .TXT document is the drill file. Sometimes there are multiple drill files.
You can zip the files together using any of a number of free or not free programs, such as 7-Zip on Windows.