Actually, you can play 1vs1, if you want. I've made it few times with my friend, and it worked pretty well for us. We've made two alliances consisting of two houses each. We tried Baratheon+Stark vs Lannister+Tirrel (Greyjoy neutral), and Greyjoy+Stark vs Baratheon+Lannister (Tirrel neutral). All you need is to change the number of castles to be captured from 7 to 13. All other rules have to stay as they are, like trading for power tokens ("clash of kings"), transporting units only through ships of the same house as of units, giving support to allied units in neighboring areas as usual (you would do it for sure), using battle cards only of that house that is involved in battle as defender or aggressor, using power tokens only by that house which possesses them. It was real fun to play this way.
Try it! Don't be totally bound by the rules. Be creative. I don't think authors would blame anybody for doing it, if they knew. When I start to understand all of the mechanics of a game and see the things that can be altered for better, I try it.
If you will have more questions about playing GoT 1vs1, feel free to ask.
This is exactly what someone tried to explain. An integral part of AGoT is the political intrigue, the backstabbing, the unkept promises, the military turmoil when alliances fall apart. In a 2-player-variant all of this goes out the window. Though you seem to miss the point that you butchered the game and turned it into something far less interesting in the process. It's not that AGoT is not playable in a 2-player-variant. It's that it's no fun in a 2-player-variant because all that this game is gets lost in the process. You might as well go back to playing Risk.
There are plenty of games where the creators tell you to make up your own "house rules". They want you to enjoy the experience. We have a house rule for playing Arkham Horror. It is called the common sense rule. If you get a card that says "you eat some strange glowing mushrooms" you have the option to say "um, no...those mushrooms are glowing, and i am not that hungry." House rules are important to game playing. It gives a different perspective and if you submit your input to the designers, they may even add your rules to future editions of the game.