At the time, each driver does not know how the other will react. The result was more hilarious than a triumph over the other. Good job no one got hurt.
As a driver, I believe in being polite when asking for right of way. Do not assume it is your right when you have given signal. Stay in your lane until after at least one or two vehicles have passed before attempting to change lane. From experience, the other driver is more likely to give way when faced with such a request than if you were to budge in rudely. It is a natural reaction to react rudely to rudeness.