Personally I usually make the distinction based on whether the process has to switch the tty to raw mode and overwrites the full screen (typically using ncurses), but it sounds like the person you are replying to makes the distinction in whether the program needs user input while executing. I guess such programs are more likely to work in pipelines or shell scripts

Unix shells “need user input while executing” in that sense. A program not being a Unix shell doesn’t make it non-CLI. A shell constitutes a CLI due to its interactive line-based user interface. Any other program with such an interface counts as being a CLI program for the same reason.