I don't believe that Visio's presentation mode was intended to behave in the same way as Powerpoint's presentation mode. It might be able to play video but I haven't explored that and I can't even see how to add a mp4 as anything more than an icon with a filename.
Perhaps you could explore how to link Visio graphics into a Powerpoint file and load the videos directly into that application. See for example
Link Visio into PowerPoint. Visio tutorial - YouTube