That is not unique to TUIs, but also possible in GUIs where the developers care, and in some games (try the GUI ("tiles") version of Brogue). You can definitely make a GUI that updates in an instant and be fully keyboard-driven, even if that may have been more common last century.
We’re comparing TUI with web browsers for good reason. I don’t see any reason to add game engines to that debate. I have never seen a business client move any application from a TUI to a Unity based UI. I’ve never even heard of anyone considering a game engine in the architecture of a business application. So what you’re saying may well be true but it’s akin to a rare mythical creature, does it even exist?
That was not what I tried to say. Brogue, like other similar games, can be played in a TUI mode, in the terminal, or with a GUI. Same game, just different UI implementations, and both tend to be about equally laggy, or usually the GUI version is probably less laggy, since you can just blit glyphs without the overhead of terminal escape codes etc to draw the same symbols in the TUI. And Brogue just uses SDL, not a game engine, so that is not relevant at all.
But your snarky reply is probably also wrong anyway, since I would be surprised if there is no business software made using game engines. Tesla is known to have used (but not anymore?) Godot for making GUIs for their in-car displays for instance. I have bought applications (not games) made using both Godot and Unity. Not saying it would be a great idea, in general, to use those engines for business applications, but people are not known for always using the best possible tools, are they, and it certainly would work in theory?
Not very familiar with Unity, but Godot has very nice GUI widgets. Same style of WYSIWYG editor like old Visual Basic or Delphi really. You drag widgets to place them on the screen, set properties, add scripts to react to different events. The entire Godot IDE itself, a very non-trivial application, is implemented using Godot's own GUI framework.