This company has built a custom configurator around a ShapeDiver model. We are not aware of precisely which technologies were involved in this process. However, it should be possible to replicate these functionalities through a Wordpress implementation
Regarding the user database, this is something to investigate purely on the Wordpress side. You can review which plugins or Wordpress features are typically used to implement a registration process, and to attach data to your website’s users, such as saved configurations for example.
Regarding the Export 2D and Export 3D functionalities, these are buttons connected to the ShapeDiver Export components, which you can read about here.
I cannot provide support regarding this topic, as this is a strictly Wordpress-related question. If you are having trouble with the implementation, I suggest you contact their support. Given my limited Wordpress knowledge, the approach you are describing sounds reasonable.
As an alternative, if you are trying to find the best way to build your website using ShapeDiver, feel free to contact our sales team with your requirements and, depending on your needs and resources, they will be able to suggest the best way forward.