If we were to make a list of the things that both types of games possess, we can try to see what makes pen and paper roleplaying games special. Let's take Skyrim as our "computer game" example, since that's the latest fantasy craze.
Skyrim shares the following elements with traditional pen and paper roleplaying games:
- an alien world, developed to the point where one can participate in it
- a single PC
- many NPCs who can react to the actions of the PC insofar as the game's programming allows
- a wide world to explore with many hidden places and side-quests and things of that nature that allow one to have an exploratory spirit
- a world that "feels" alive, in that it responds somewhat realistically to change
- strict rules that are enforced by the game-engine (or the DM in our PnP case)
- enemies which think as intelligently as the game-engine (or DM) can allow
True adaptability doesn't mean that once you've completed a quest it isn't available anymore, or that the farmhand you helped out marries his beau and has no more to say to you. True adaptability means that the world continues to adapt around you based on your own actions and, in the case of a certain kind of game (my kind of game) regardless of your actions. I cannot realistically foresee a day when that can be achieved by a computer. Unfortunately, the limits of computer games tend to preclude this sort of endless forward motion. At some point, you reach the end of the quest or the end of the dialog that the programmers created and the world grinds to a halt. This is a sort of virtual adaptability that has only enough depth to give you the feeling of change. Don't press it, though, or the curtain will soon be twitched aside to reveal the limitations of the system.
An expanding setting is related to true adaptability, but it applies to the world at large instead of a single place in specific. While adaptability may govern the actions of the farmstead you are on (you could stay there forever helping out these folks, because the DM would continue to provide you with new situations and scenarios) expansion governs the wider setting at large. When you reach the end of a map in a video game, you generally are forced to turn around. When you reach a blank spot on the map in a pen and paper game, your DM usually says "Alright, we'll resume this in a few hours or tomorrow or next week as I draw up some new maps." The setting continues to grow as long as you are interested in playing in it.
Lastly, other players is the most minor issue out of all of these, since there are roleplaying games that allow for other players. However, the nature of game design tends towards storytelling with all that this implies: main characters, plot arcs, and things of that nature. It's never really fun to play a sidekick in a story when you are explicitly a side-kick. Your actions don't really matter, it is the protagonist PC who can change the world. That's a kick in the teeth for realism and ego both. In a pen and paper game, no one has to be the protagonist. The entire idea of a protagonist is sort of counter to the experience because, as I've said before, like life the story of a D&D game can be what you make of it rather than something told by the DM.
Now, what is it that allows pen and paper games to achieve these three harmonious unities? The presence of the DM. The DM is not a computer that sits there to arbitrate rules. If that's all you're using your DM for, you should just go and play a computer game. Computers do that better than people do, and they don't have to spend time flipping through books or getting challenged to make sure they're right. The primary job of a DM, then, or any referee, isn't to be a repository of rules-knowledge (it helps) but rather to hold in his mind's-eye a living growing world and somehow transport you, the player, into that world.
Remember that next time you're about to tell your DM that you "deserve" a magical item or two.