Is this equivalent to the game of chicken?
As you stated the strategy set in the traditional chicken game has two elements and in the Akagi version it is an interval, so there will be no bijective mapping between the two.
If I misunderstood and you are using a different notion of equivalence please clarify.

Also as you state in the Akagi version there are weakly dominant strategies but in the traditional version there are none. I believe the story of the traditional version is rather about two cars driving towards each other and you have to decide whether to swerve at the last moment or trust that the other driver will. Even if you were to extend the strategies to allow swerving before the last moment this game would differ from the Akagi version, because here not swerving at all is better than swerving at the last moment if the other driver swerves at last moment whereas swerving at the last moment is better if the other does not swerve at all, hence there are no weakly dominant strategies.