Game of thrones played by two
As you said yourself, one of the key mechanics of the game is forming alliances and breaking them eventually, all for your own benefit. With two players, you already know who will be your enemy at all times, and so do they, so there's no need to ever ally with the other player.

In addition, the map is too large to be played by only two factions. You can see that the game already takes out major regions in the south for less than a certain amount of players, but there's no such variant prepared for less than three players.

Not all games can be house-ruled to fit a certain group of players, and this is one I'd stay away from trying to do so. The closest you can probably get to making it work is by giving each player multiple factions, however due to the mechanic of forming alliances, this will likely not give you the game experience you hope for.