Hi,
I just stumbled on this topic while searching for something else.
Please note that this has always been possible with HikaShop.
You want to either create a "color" named characteristic with as values the html code for each square image via the menu Products>Characteristics. You'll also want to change the "characteristic display method" option of the configuration to "radio".
An alternative is to not use a variant but a custom field of the table "item" and of the type checkbox, or radio, or dropdown with, similarily to the characteristic, the html code for each square image.
After you configure the characteristic/custom field for your product(s), on the product page, you'll see a radio list with the color images, one per radio.
If you don't want to display the radios, so that it looks exactely like the link of your message, just add some CSS code to hide the characteristic/custom fields radios and that will do it.
Bonus points:
After having set that up for your products details page, you can even have such color select as a filter on your products listings.
To do that, create a filter with the display type "radio" on that characteristic/custom field via the menu Display>Filters. Similarily, you'll be able to hide the radios next to the color images with a bit of CSS if necessary.