As you found, the exit is between chutes. So you should find another way to reach the stair.
To exit the floor, you should try another door, travel through many traps, warps and chutes, and defeat some groups of monsters. Mapping is too difficult because all B666F is a trap. Most of all messages are incorrect. But exactly there's a correct way to exit. Don't forget the secret door.
If you give it up, cast EMERGENCY EXIT. That's a last resort.
> Sir, congratulations on creating a great game.??I have been trapped in Basement Level 666 for two weeks.??I have mapped it all, I believe.??How can I exit???It says the door on the Left is the exit, but chutes in that room make me fall before I reach the square that appears to have the exit.??Is using the spell "Emergency Exit" the only way???I know that Teleport does not work on this level.