A GUI that is built with Text, and intended to be used in a Terminal, is what a TUI is, colloquially AND definitionally.
What do you think qualifies as a TUI?
Of course you can use the primitives of TUI, especially with mouse support, to reproduce a large amount (if not all) of the standard GUI interaction paradigms.
But it's bizarre, and missing the point from a UX perspective.
As an extreme example, we can imagine a program that displays the borders of a 40x15 "window" in the middle of a console, with box-drawing characters, putting a "close box" in an upper corner, with text like "File Edit Help" in the top left. We can imagine it responding to a click on the "File" text by popping out a "menu"; we can imagine a drag starting from the "title bar" causing the window position to be update (and the entire terminal window redrawn).
A lot of those kinds of functions, ironically enough, might make sense for a TUI editor implemented as a TUI (except the "windows" might just be understood as panels where the ultimate program displays parts of its output). But as an emulation of GUI windows, it'd be a strange, impractical novelty.
Even in your example, it's pretty clear cut. If the window is built with text and served in a terminal emulator, it's a TUI. If you build it with a graphical framework that now needs X11 or whatever, it's a GUI.
This is just needlessly pedantic.
The issue is not the text. It's the WIMP interface.
It's a GUI that works over SSH. There is a very valid use case for that.
But if this thing requires you to just tab a lot through lots of pointless and rarely used fields to get to a "button" so you can activate it, because it's really all designed to be used with a mouse, then it's a bad text-based UI.
There are some incredibly good text-based UIs around, some going back to mainframe stuff from the 70s. Most of them are optimised for speed of control via keyboard rather than for looking pretty. Almost none of them would be quicker to use with a mouse.
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.