Hi Allution,
I just checked the website you referred to: worldofharry.com
worldofharry.com is based on WordPress + Woocommerce for handling ecommerce + a custom theme for the storefront. We have what's needed to create a similar website like this one, based on your needs.
Please drop me a PM with more information about your project (niche/market, product types, number of products, currencies you'd like to accept, etc.) and let's discuss this even further. Or simply email the information to
hello@adfountain.com and I'll get back to you ASAP.
Best