You change the style in the same way you change the style of anything on your site. You could, for example, edit your theme’s style.css or you could use the Customizer’s “Custom CSS” feature.
The inbuilt styling is not meant as a “works for everyone” solution but is an example of how you could style the page. It is anticipated that it will work for most people out of the box but there is a likelihood that it won’t fit your site’s design in which case you can either add style overrides to the inbuilt style or you can turn off the styling entirely and write your own styles from scratch.
If you require customizing the HTML output of the listing then you need to copy the file from wp-content/plugins/a-z-listing/templates/a-z-listing.php into your theme’s root folder and edit appropriately. This file follows a WordPress-style “the loop” mechanism extended to support the separation of posts into groups by letter.
