Those use TERM/TERMCAP environment variables and some educated guessing reading stdin/stdout/stderr behaviour to figure out what terminal you're using, search for said entry in terminfo/termcap database, and finally invoking native terminal behavior or simulating it with other terminal behavior.
In theory, one could "just implement" an alternative terminal, and put said simplified entries in terminfo/termcap database and things will be all fine.
In practice several of those ANSI escape code behaviors are hard-coded and everyone pretends everything is "at least as capable as xterm" (a oxymoron, given that xterm is one of the most capable and feature-rich terminals around), so you're also gonna have to implement a converter from "xterm ANSI" to your alternative terminal system - sort of how winpty does convert Win32 terminals conventions to ANSI ones.
Then we're back to the starting issue in this converter.