That doesn't seem to be the case in my setup. The extracted files from the Dell site is simply the Setup4.1.19.0.exe with a version.txt file which when I run does a full install once more and adds the shortcut once more. If that's what you mean, then yes the file is still present after the update utility removes it.
If I run it again, I do get the first time screen where I have to agree to the EULA, but after that it's back to the same message about needing the latest graphics driver. I'm currently running 10.18.10.3379 released 12/18/2013 which I got via Windows Update, so not sure what the deal is there (which, btw appears to be newer than what Intel has available here.)
Interestingly though, I was able to access settings this time around going through again as I write this, and sure enough I was able to see the P2TV again. The application is being really flaky (shocker, I know), but it is seeing my device now. Unfortunately, it's not connecting for some reason and the button to do so is grayed out:
Toggling legacy devices in settings doesn't seem to make a difference one way or another and mine should not be legacy (P2TV3000) which is certified on the Intel site last I checked.
Also tried removing the device under Devices in Control Panel and re-adding there just in case, but doesn't seem to affect the utility.
Again, more hoops than should be necessary *sigh. As always, feedback is appreciated in hopes of getting this resolved and so others may be assisted too.