It is true that too many clicks will put people off, but you have such a massive catalogue you need to break it down a little.
The point I tried to make is that when you give people a choice of what to click next you make it as obvious as possible what they are likely to see if they do click the link.
To do this it would be helpful to have an informative alt text on all the links, example montages of products next to all the links, a small description of what to expect in 7 words or so, anything to help the visitor to know what to expect by clicking rather than clicking and hoping for the best.
People will be happy to click links if what they get when they do is what they expected.
An example of this on your site is Cat and Dog Gifts. This ambiguous. It is gifts for animals or for animal lovers. Suggested change would be Gifts for Cats and Dogs and some for their owners too. Pet beds, lead hooks and blankets.
In this way people will not make clicks they don't need to, reducing the time it takes for them to find the perfect gift and increasing the chance they will stay on your site and not click off to one which is better designed and easier to use.
I think that by putting all your images on the left it swill make browsing a lot easier for customers and maybe then you could get away with a long page.
Do not, however, turn your long page into 1of4 pages type of layout where customers must chew through page after page of much of the same without being able to remember where they saw the one item they fancied.