So, its not really possible to tell what program was used to build this site by just looking at the site and/or HTML source, unless the developer left behind HTML comments that would indicate what was used.
For sure, there is server-side programming. The web application could be customized PHP, or it could have been developed with some type of eCommerce web application that generates the code for the developer.
It is the same script type used to make all those personalised roadsigns
ajax using imagettftext() to create a transparent overlay. This one is more sophisticated there is a texture map applied to the generated image that closely matches the underlying tshirt.
The layer does not alter the tshirt image, just sits over it