... did you write this code? It looks like it does exactly what you're asking for - simply add new pages you want to be linkable in other_files/[newpagename.php]. Then you'd call it with index.php?page=newpagename.php
Just a word of warning, though - there are some security issues with this code, potentially. It helps that you're in other_files but you could still most likely execute directory traversal attacks and just have users generally poking around where they shouldn't be. You may want to decide on something more like this, if you're set on a variable-based page include:
$allowed_pages = array('index.php', 'about.php', 'contact.php');
if (isset($_GET['page']) && in_array($_GET['page'], $allowed_pages)) {
include('other_files'.$page);
}
else {
echo 'Invalid page passed.';
// could also default to including index here, if you chose.
}
That would prevent users from passing in data that could potentially reveal sensitive information or run malicious code. Just a thought.