Answer

As I understand it, the concept of an obligatory war is a war waged for the sake of some commandment, such as conquering the Land or wiping out Amalek. The obligation to fight stems from a commandment of the Torah.
By contrast, rescuing Israel from an attacking enemy is simply a war of self-preservation. Even if the Torah had not introduced this, the obligation/right to wage such a war would still exist. Indeed, as far as I know, the Torah does not introduce such a war anywhere. It is simple logic that every nation has the right and the duty to defend itself.
Maimonides (Laws of Kings 5:1) includes this war in the list of obligatory wars because it too does not require permission from the religious court (see there, 5:2). Moreover, if we have no king and our lives are simply in danger, is there not still an obligation/right to wage such a war?
And see there in 6:4, where he mentions as obligatory wars only the war against Amalek and the seven nations, and not rescuing Israel from an attacking enemy.