OK I found a fix for this Problem!
Basically follow the following Instructions provided by @Nei
Sorry for my english language in advance. I reinstall the game twice and it works for me twice. This is what I did :
I opened the PowerShell as Administrator (in start menu, type Powershell, right clic on it to open as admin).
Copy this line in it :
cd "C:\Program Files\ModifiableWindowsApps\pso2_bin"
cd "C:\Program Files\WindowsApps\Mutable\100B7A24.oxyna_184.108.40.206_x64__wyfsmff9ynw7j"
It depend where your files are installed (for me, I used the second line only). My game is installed on C and D... If your game is install on
other place or other folder, change it of course.
Next, when you are in the folder on PowerShell, you copy/past this :
Get-Acl pso2launcher.exe | Set-Acl pso2.exe
Get-Acl edition.txt | Set-Acl otp_notice_na.rtf
No errors messages ? it's done, rights are changed.
Return back on the launcher, launch the game. Update starts again but this time, no error message anymore. And the game starts
It works for me and for my friends, so I hope it works for all