That particular screen is from Task Manager's File
-> Run New Task
and exists since Windows 7.
This check box doesn't exist on the standard 'Run...' box from Win+R, although you can get to this screen by using Ctrl+Shift+Esc, Alt+F, N if you wish.
Otherwise, you can run things from the Start Menu as admin by holding Ctrl+Shift and pressing Enter.
You can disable UAC and use an administrator account to remove this protection, although this is a fairly dangerous practice as you will have no defence against any program with a malicious intent. You can find the option under User Accounts
in the control panel.
More information in this question I made here.