A Game Genie code does exist to enter this debug menu. See the beginning of
this page for how to use the code to get to this debug menu. Essentially, it requires the code to be activated before reading certain signs in the game, which causes some other text from the game to display until the debug menu is reached. (then the code needs to be deactivated, since it causes weird/bad things to happen elsewhere)
There are actually two debug menus in this game, but at this time the second one can only be accessed via a code because it is special and probably coded separately (to compare:
debug menu 1,
debug menu 2.
The second debug menu is not very useful, really My bad, I didn't realize "view map" enabled changing flags and stuff too, along with accessing the first debug menu and rolling the staff credits). The debug menu used in this TAS uses the same menu system as every other in-game prompt (which uses the text window display). This makes it accessible through the tent glitch, since the pointer to text to display ends up pointing to a junk value and, through manipulation, can eventually be advanced to where the debug menu is.
So this TAS gains access to this debug menu through a glitch rather than using a code. But it almost seems like the code does something similar to the tent glitch, since it does not grant instant access to the debug menu but, rather, makes other text appear first.
Of course, you cannot use Game Genie codes in a TAS. They are not saved when recording a movie anyway.