I checked your website and I can see that your template doesn't use bootstrap system for responsiveness.
The responsive system in HikaShop to switch automatically between 4 and 1 column based on the size of the screen is only compatible with bootstrap system since that's the default system on Joomla 3.0 and that everyone, extension and template developers, are encouraged to use it.
Since your template doesn't support that, you should keep that option turned off.
As Xavier said in his first message, it would require custom CSS to change manually the width of the elements based on the size of the screen.
For example, you could use something like that:
@media only screen and (max-width: 800px) {
.hikashop_product{
width : 100% !important;
}
}
and all the screens below a width of 800px would get the product listings on one column instead of 4.