Example:
1: create a new single player word with cheats disabled.
2: in the world, open the Game Menu (press ESC)
3: click "open to LAN"
4: change "Allow cheats" to ON.
5: click "Start LAN World"
6: In chat, type "/gamemo"
7: Press TAB
8: Notice that it does not complete to "/gamemode" as it should (since cheats are enabled). It also only displays the commands for cheats disabled.
9: Now type the correct command in chat, "/gamemode creative" and press ENTER.
10: Notice that the command works, which means that the player has access to it.