The correct way to delete all files older than 2 days in PHP

You should add an is_file() check, because PHP normally lists . and .., as well as sub-directories that could reside in the the directory you’re checking.

Also, as this answer suggests, you should replace the pre-calculated seconds with a more expressive notation.

<?php
  $files = glob(cacheme_directory()."*");
  $now   = time();

  foreach ($files as $file) {
    if (is_file($file)) {
      if ($now - filemtime($file) >= 60 * 60 * 24 * 2) { // 2 days
        unlink($file);
      }
    }
  }
?>

Alternatively you could also use the DirectoryIterator, as shown in this answer. In this simple case it doesn’t really offer any advantages, but it would be OOP way.