Hi,
In your checkout page, you can see the message : "Registration not allowed"
If you do not allow the registration in your website, the customer won't be able to create an account and finalize the order.
If you don't want HikaShop to do the user creation, you can just put a login instead of the registration.
These options are in the HikaShop configuration, section "Checkout > Login & Registration".
Regards,
Jerome - Obsidev.com
HikaMarket & HikaSerial developer / HikaShop core dev team.
Also helping the HikaShop support team when having some time or couldn't sleep.
By the way, do not send me private message, use the "contact us" form instead.