The 1603/1605 errors we see there are typically a previous other installation stuck, or a problem in the Windows update/install processes.
If you see
msiexec OR
Paradox Launcher running in Task manager-processes, kill it and try this launcher install again please.
If still no good, do you see Paradox Launcher v2 in the Windows Control Panel to uninstall? If so does it uninstall cleanly, or get an error doing that? You can use this MS tool to clear the stuck install/uninstall:
The Program Install and Uninstall troubleshooter helps you automatically repair issues when you're blocked from installing or removing programs.
support.microsoft.com
THEN Please try the clean launcher reinstall again.