Hi,
That page is still quite relevant. It's just the carousel system which has been changed to use one which is responsive, while the one on our demo website is the old one which wasn't. So the look is a bit different, but the capabilities are roughly the same and the settings are still the same.
I can see that you've added custom CSS code in your template
.hikashop_product_stock_count {display: none;}
to hide the stock.
I can see that this CSS is present on the product page and hides the stock there.
I don't know why the template doesn't also add it for your homepage. If it did, it would also hide the stock in the carousel. Maybe you need to clear your template's cache ?
However, note that this just hides the stock for the user, but he can easily look into the HTML to get the stock.
If you want to really remove that information, the best is to add a translation override for the translation keys NO_STOCK, X_ITEMS_IN_STOCK and X_ITEM_IN_STOCK :
www.hikashop.com/download/languages.html#modify