Mscion, I believe the reason for this is HDCP protection is enabled. you would have to edit the stagefright lib file I believe but ive seen people get it to work by a simple build prop edit. There is a thread on this which I used to get mine to work with Lean Kernel I believe it was on my Note 3. I will try to find it for you guys and post the link. I think it may be in the S4 forum. Give me a little time and I will find it. There is some good info in this thread about screen mirroring.I think you are correct here. I happen to have an allcast dongle socked away in a drawer (hadn't used it in quite awhile). My phone recognizes the dongle but refuses to connect. I'm wondering if it may be an issue with a build.prop setting. Will try to take a look but figuring this out may be above my pay grade.
EDIT: You might want to check out this thread.
http://forum.xda-developers.com/showthread.php?t=2281912
It states that allcast only works with stock kernel. But in the last few posts (#70) someone mentions that they had to "forget" their home wifi to get it to work. I can't tell if they were using stock kernel at that point. I will try tomorrow.