The 3DM file format can represent 3D NURBS and polygon mesh geometry, and can be read and written by the openNURBS toolkit: http://www.opennurbs.org.
While the example on the Nike web site looks 3D, it appears to me to just be a set of 2D rendered images that can be swapped out as the user customizes the shoe.
You could render each piece from within Rhino, and then build a web application to allow the user to customize, if you wanted to copy the model that Nike used.
Developing a professional web application to customize content like Nike did is not something that can be written down in a simple answer to your question.