2012 R2 server does not have domain administrator as a user

Is it joined to a domain?
Is this joined to another domain or is it a standalone DC?

The domain users (including domain groups and user) do not show locally unless you are checking group members or ACLs assigned to resources such as files/folders. Where are you checking? Please post some screenshots

yes part of a domain.  See attachments

No idea why you added the user... I never do that.  The Domain Administrator is part of the Domain Administrators group.  By Default, this group is included in the local computer's "Administrators" group.  So thanks to group membership, you have the administrator rights.

Would have been helpful to post the PowerShell window's errors (including the window title).... my guess is that you weren't running the Powershell command as an administrator.  (By default, even if you're an admin, you don't run things with admin rights for security).

Why doesn't the domain admin show in the securities properties?

Remove-Item : Cannot remove item C:\Windows\System32\Lock64.dll: Access to the path 'C:\Windows\System32\Lock64.dll'
is denied.
At C:\removalscript\Tricerat v4 Removal Script.ps1:337 char:5
+     Remove-Item $env:windir'\System32\Lock*'
+     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    + CategoryInfo          : PermissionDenied: (C:\Windows\System32\Lock64.dll:FileInfo) [Remove-Item], UnauthorizedA
   ccessException
    + FullyQualifiedErrorId : RemoveFileSystemItemUnAuthorizedAccess,Microsoft.PowerShell.Commands.RemoveItemCommand
Remove-Item : Cannot remove item C:\Windows\System32\LockScreenContent.dll: Access to the path
'C:\Windows\System32\LockScreenContent.dll' is denied.
At C:\removalscript\Tricerat v4 Removal Script.ps1:337 char:5
+     Remove-Item $env:windir'\System32\Lock*'
+     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    + CategoryInfo          : PermissionDenied: (C:\Windows\Syst...reenContent.dll:FileInfo) [Remove-Item], Unauthoriz
   edAccessException
    + FullyQualifiedErrorId : RemoveFileSystemItemUnAuthorizedAccess,Microsoft.PowerShell.Commands.RemoveItemCommand
Remove-Item : Cannot remove item C:\Windows\System32\LockScreenContentHost.dll: Access to the path
'C:\Windows\System32\LockScreenContentHost.dll' is denied.
At C:\removalscript\Tricerat v4 Removal Script.ps1:337 char:5
+     Remove-Item $env:windir'\System32\Lock*'
+     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    + CategoryInfo          : PermissionDenied: (C:\Windows\Syst...ContentHost.dll:FileInfo) [Remove-Item], Unauthoriz
   edAccessException
    + FullyQualifiedErrorId : RemoveFileSystemItemUnAuthorizedAccess,Microsoft.PowerShell.Commands.RemoveItemCommand
Remove-Item : Cannot remove item C:\Windows\System32\LockScreenContentServer.exe: Access to the path
'C:\Windows\System32\LockScreenContentServer.exe' is denied.
At C:\removalscript\Tricerat v4 Removal Script.ps1:337 char:5
+     Remove-Item $env:windir'\System32\Lock*'
+     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    + CategoryInfo          : PermissionDenied: (C:\Windows\Syst...ntentServer.exe:FileInfo) [Remove-Item], Unauthoriz
   edAccessException
    + FullyQualifiedErrorId : RemoveFileSystemItemUnAuthorizedAccess,Microsoft.PowerShell.Commands.RemoveItemCommand
Cleanup failed. Manual cleanup required.
PS C:\removalscript>

That's a copy and paste, not a screen shot.  A screen shot would show me the title bar:
A picture is worth a thousand words.  A copy and paste only 100.

here you go

Ok, so the next question is, does the Domain Admins group belong to the local Administrators group on the computer?  Check in Computer Management.

nope.  How do I add it?

I was incorrect.  Domain Admins is there

What's the permissions on the files in question (that you're trying to remove)?

see attached

That fixed that problem, but there are more.  See post below

https://www.experts-exchange.com/questions/29040141/Windows-server-2012-R2-permissions-on-services-get-Access-denied.html

Thanks