Hi,
As you can see, there is no "ReCaptcha" in your registration form, so it is logical that the plugin can't validate anything because the user can't enter anything.
We don't which version of HikaShop you are using, which precise version of Joomla you are using or which "System ReCaptcha" plugin you are talkng about.
But for most I can see, you have du disable it if you what that the registration works good.
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.