How did he do this?

Uh … I don’t know what you mean. They all just point to categories that all look the same. That’s just normal WP.

Ok sorry I’ll need to be more clear…

On my site, the links at the top point to “pages”, he has them pointing to Categories.

How is this done?

Oh that ??

In your header.php, you probably have this
<?php wp_list_pages('title_li=&depth=1'); ?>

The bit with title_li may be different.

Just change that to
<?php wp_list_categories('arguments'); ?>

Where ‘arguments’ is whatever you have in for list pages.

See https://codex.www.ads-software.com/Template_Tags/wp_list_categories for details