How about this: Is it role playing if you have no choice in how things should be done?
In Tomb Raider, you must find the key that opens the door that hides the lever that opens the exit. Sure, you can take the passage on the left or the passage on the right to get there, but ultimately, you are solving a strict puzzle. There is no other way to do it. And any optional extras along the way mean little in the grand scheme of things. So you get a few extra bullets or a new gun. No-one cares two days later that you just robbed a gun store.
In Deus Ex, while there is one ultimate goal, there is usually numerous ways to complete it, assuming you want to. Combat, stealth, street-smarts, underworld connection, and hacking all provide an answer to each puzzle. You have options! And in each case, the results of your actions have lasting effects. In Deus Ex 2, you can kill people or knock them unconsious. I have a moral objection at killing anyone unnecessarily, even though they're just polygons. So when I was asked to assassinate a lawyer, I really had to think twice about it. After killing him for my cheap reward, I discovered he played a key role later in the game.
