As classes don't exist as you mentioned, the only way to give yourself the 'feeling' that you are playing a character of a class is by forcing yourself to play that way. Everybody has the sneak skill, it's a basic skill now. You just have to get those other skills that match your class best and play in the style of the thief.
As far as I gathered it, the game enforces nothing on you, nor do you get the game to enforce this upon you. Only you yourself can enforce playing like a thief.
