As requested by this comment I have published the code for the Popular Links plugin to appear on the public side.
Copy this code and save it as popularlinks.php
Upload it to the /pages directory of your YOURLS installation.
It will appear on your site as YOURLS-SITE/popularlinks
As with the plugin, you can customize it by editing the values
1000 means the number of days you are selecting from the database
5 means the number of links you are selecting.