It can embed any media file but it is not a media player. So it depends on the visitors browser what happens with that media file. Images are no problem for almost all browsers (yes: almost. there are text only browsers!) but MP4 files might be less supported specially on mobile. Still, most desktop browsers will have no trouble with a link that opens a fancybox in iframe mode like this:
<a href="url://of.your.file.mp4" class="fancybox-iframe">watch this</a>
(Don’t forget to activate the “iFrame” option on your Settings > Media admin page.)
But if you want full cross platform support, you are better off hosting the video on a video hosting platform. Or yo could try the WordPress built-in video player (MediaElements) by switching to the Text tab when editing your page/post and pasting the following example there (replace the URL with an actual video file URL):
<a href="#myvideo-1" class="fancybox-inline">watch this</a>
<div class="fancybox-hidden"><div id="myvideo-1" style="width:480px;height:360px">
[video src="url://of.your.file.mp4"]
</div></div>
(Don’t forget to activate the “Inline Content” option on your Settings > Media admin page.)