I believe though he could not become King, he could not turn ignorant and blind eye to what would happen to the throne of Hastinapur. Besides, I am sure he did have his wishes to become King and if you have the desire, you automatically consider and take the responsibilities along with it.
He was a part of politics of Hastinapur, he was also an integral part of all decision making. I simply believe, he loved this throne too much. Not out of greed (because IMO he was anything but greedy) but out of attachment.
So when the time came for war, he fought in the side of Hastinapur as that was the throne he had committed himself (not due to oath but due to his own personal attachment and ambition) to. He also considered himself responsible for what happened to the throne. So I think this was his decision.
I do understand his oath did not include serving Hastinapur in anyway. But if he is not the King, and if he is taking all the decisions that a King ideally should, is it also not his responsibility as per the moral terms of Dwapar Yug to fight for Hastinapur's side? I think it is something he bestowed upon himself. He loved his soul, clan and throne too much to fight against them.