Hi,
You're right, it works on the link you gave too.
I have the impression that it can work only if the URL is SEF.
Otherwise, when you edit your cart, the sliding module does not update the cart content, it don't receive the notification like a "real" HikaShop cart module.
I don't know how it works but I don't think that they have an integration with HikaShop.
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.