it looks/sounds like you needs to find a shopify theme that mimics that behavior. If you search through google or shopify, you can find tons of theme options. Or go to 99designs and see if someone wants to create one.
This is an order form customization , shopify help docs even has an advanced tutorial for it.
Your example has a lot more features.
However if your products are not already sold by the pack you will either an app to manage bundle pricing and inventory or restructure you product data.
Contact me if you need to get it for your business, or need to work out details.