The buttons on that site appear to be working fine. However, since you're using the non-javascript version of our button codes, the cart is opening in a new "popup" window/tab rather than the nice overlay our standard cart uses.
Different browsers and settings may have different ways of treating the popup cart, so depending on that browser behavior and the buyer's browser settings, it may not be obvious that anything happened when clicking the Add to Cart button. For instance if the popup window or tab doesn't get brought to the front, the buyer would need to notice that a new tab had appeared in their tab bar or a new window had appeared in their taskbar.
If you use our standard button codes and make sure to include at least one block of View Cart code on every page that has any number of Add to Cart buttons, that should allow our standard overlay-style cart to appear "inside" the seller's own page, and buyers who have javascript disabled in their browser would still get the cart in a new window/tab as our standard buttons operate that way in "fallback mode" when javascript is unavailable.