The OP is not complaining about anything! I really wish people would read the question and if they have nothing helpful to add then not bother replying!
The question was simple, the phone can happily play a 4k video on its 1080p screen (It is not a 4k screen!) However when MIRRORING the 4k video will not play. The screen being mirrored is a 1080p screen so as such the video being played (despite it being a 4k video) is also being shown on the phone at 1080p yet it will not play. You are mirroring the screen not streaming the video in its native resolution. My view would also be that it should just mirror the screen without issue.
Can you provide a little more info;
Are you definitely mirroring the screen? Can you see your Launcher, an actual copy of your phones screen? My guess is that you are probably just sending files over individually which will probably not work.
If you are definitely mirroring, are you doing so wirelessly or over a cable etc...