First of all, it's not easy following this video which keeps flashing by like a neon sign. In any event, the solution is not to alter the link dialog but to handle this exception in the editor's pre-processor.
The pre-processor function you need is edit.php:_preprocess(). At line 354, you will find:
$this->xhtml = $this->_render_xhtml($text);
Replace it with:
$text = preg_replace('#\[\[m-files://(.*?)\]\]#ms', "MFILES_OPEN$1MFILES_CLOSE",$text);
$this->xhtml = $this->_render_xhtml($text);
$this->xhtml = preg_replace('#MFILES_OPEN#ms', "[[m-files://",$this->xhtml);
$this->xhtml = preg_replace('#MFILES_CLOSE#ms', "]]",$this->xhtml);
Then, simply enter your url into the CKEditor as you would in the Dokuwiki editor:
[[m-files://show/EEA8B314-D583-4F59-B0AE-08A6B9434320/0-282?object=3F91BD85-2F92-4CBF-B999-13B932DE1FC9]]
If you wish, you can give your file a short name:
[[m-files://show/EEA8B314-D583-4F59-B0AE-08A6B9434320/0-282?object=3F91BD85-2F92-4CBF-B999-13B932DE1FC9|short_name]]