How to force to run any setup/program/file without admin rights?

The only way to remove the rights required by programs is to completely re-write them and / or the OS, there is no other way.

This was also the case in older versions of windows NT style operating systems (Win 9.x had no security at the system level). windows XP faked the old way of working in the 9.x windows versions, for the home market, by making every user a full administrator, which made it look like the users did not need admin rights to install Programs, Drivers , Printers Etc. - They did but it was not obvious to the user.

It was actually common practice in NT, Win2000 and thus XP to create all users as Administrator accounts and leave the correction to the System / Server Admin to reduce the rights to safe levels, or leave them as local rights and constrain them at the network level.

Just to try to explain a little clearer

The rights, (or lack of rights) that are triggering the messages you are receiving are a part of the operating system rather than the actual programs. There are many examples that show this in the way that a program behaves differently if the program is ran by an administrator than when run by a non administrator - if the program is asked by the user to perform some task or access some file which are given Admin Only protection it depends on the user rights whether this action is completed, not the programs limits. Some programs can only work as an administrator due to the jobs they are designed for and these will normally trigger the admin elevation required message directly to save later checks and processing but most are triggered by the OS when the program attempts to access a protected object.

The reason for the amount of protected objects ( files, processes, folders, Etc), has risen dramatically in the later versions of windows is due to the need to defend against the modern sophistication of malware but a lot of access restriction has always been there, just hidden by the subterfuge of all administrative users.

The link you show is not a major bug in that I am confident that given access to a physical system most cybercriminals and IT Professionals could quite easily gain access to the contents of the hard drive - encrypted data would still be safe although the subtle addition of physical removal and remote storage of the hard drive is even better and standard practice in truly secure systems - of course the value of the data itself is a major factor in the need for security level employed - it's unlikely that any criminal will break into my property to steal to personal info

One way that may work is to remove all security on every object that can be changed - ie every file, folder, and registry entry in the system ( a task almost akin to making eggs from an omelette). but this would have to be performed by the hidden administrator account in order to circumvent the added security performed by the TrustedUser account.

if you have a specific activity that is causing you an issue, (or just annoyance), changing the permissions on specific objects, may remove the restrictions with an acceptable level of work although this might take a fair amount of trial and error to achieve as any modern OS is a complex system

The admin rights system is the very permission you are requesting but is so designed to protect you and your system from those criminals that want to gain access to your system to rob you. I know that my personal bank account is not something that would allow a criminal to live in luxury, but empty a hundred or a thousand or a million such accounts and that is worth their efforts.

They are to blame for the security hike in recent software - yes it's a right royal PITA but I consider it necessary for my ease of use over what I always used and I understand the developers adding it these days as I'm sure I could foresee an awful lot of litigation from people whose systems are hacked if the security was not in place - Sad but the world we live in I'm afraid

Some developers are more compliant to Microsoft's development Guidelines, (rules), than others. I've forgotten the number of times that programs fail with a new OS or even system update due to the fact that a developer made a direct call to a system process rather than use the designated MS system variable, (which changes the location correctly when it actually changes).

I think there is a similar error in some programming for the admin requirement

I've seen games and other Utilities that have an admin requirement due to the developers being to lazy to move the storage location for the game parameter settings (.ini file) from the Install folder in Program Files to the user AppData folder where the permissions are correct ( this has been a "requirement" from before the release of XP and the end of the 9.x line).