Hi,
The refresh actually works there if you enter the new value in the input field and click on the refresh button.
From what I can see, it only doesn't work when you use the - and + buttons to change the quantity before pressing it.
And if I check the console of my browser when I do so, I can see some javascript error when using the refresh button.
And I can also see that the javascript of this button has been customized (which is why you get that error) :
i.imgur.com/UlUfyi9.png
Apparently, that cart module is customized by your template or something else.
I suppose that if you rename the file templates/YOUR_TEMPLATE/html/com_hikashop/product/cart.php via FTP, it will then work fine, which will confirm that the issue comes from some customization in that view file override.