Would you say old DOS applications like Borland's Turbo series of compilers were not TUIs? They ran in the console but had menus, mouse support, dialog boxes, etc...

How about those text games that used ASCII art and you typed in commands like "look" and "go north"?

I would say using text mode is the primary requirement for a TUI. The other requirement being some kind of human-machine connection, IE a User Interface.