I've just done some testing after editing php.ini to increase "max_post_size" and "upload_max_filesize" so I could upload an MP4 file.
If you add "post_mime_type=video" and "size=icon" to your query you will get a gallery with an appropriate icon for the file and the caption displayed beneath it. When you click on the icon you get an "attachment page" with the full description beneath a link to the video. Click on the link and the video will play in Quicktime or some other broswer video plugin. You can also add "link=file" to the gallery to bypass the attachment page.
I think [mla_gallery] does the right thing for its part in the process. I'm going to mark this issue resolved.
If you have any other questions or problems, let me know. Thanks for using the plugin!