Sorry for the delay, had to do some digging. Sounds like the original uninstall method used in this case did not clean up the registry keys associated with the launcher. This means that at some level, Windows still thinks it is installed. This link goes into some of the boring details behind the way Windows Installer stores info about installations it thinks are valid.
I suspect we’ll have to cleanup some registry entries to get you past this issue. The hard part will be finding the right ones to remove since Windows uses arbitrary GUIDS to store the info we are after. You may have some luck with third party registry cleaners like Microsoft’s FixIt but I’m not sure how many run on windows 10.
Depending on how comfortable you are with making registry changes, one of the first steps would probably be to open regedit and navigate to HKEY_LOCAL_MACHINE\SOFTWARE\Classes\Installer\Products. Once there, ‘Find Ctrl-F’ anything launcher related to see if you can find an Unreal Engine or Epic Games launcher entry. Let me know if you have it and we can try a few things.