Hi Kevin
I have no such issues (in Citrix receiver) running .mp4 videos in courses I've output from Articulate Storyline.
Storyline content is Flash-based when run on a desktop browser, so it's using a Flash-based video player rather than the browser's built-in HTML5 video player that Adapt uses.
There are a whole range of issues as to why HTML5 video isn't working, not an easy thing to debug I'm afraid. First thing I'd do is check the that MP4 mime-type is correct defined on the server the content's running from.
It could also be the Citrix/network setup that's blocking it - I've run into that before too. Same video file but trying to load it as HTML5 video was blocked, loading it as Flash-based video no problem.
Flash-based video has been around a LOT longer than HTML5 video so you often find it works when the other doesn't.
Seeing as you know that using a Flash-based video player works fine then you can force Adapt to use Flash-based video by default by changing this to "none". It will still use HTML5 video on operating systems that don't support/have Flash installed, I guess the question is just whether it works OK there or not?