There is definitely a difference to discuss, but simplified it still states "Unless you change your behavior, you need to go", as suck, I don't feel that "fired" is inaccurate.
This feels reductive. He was asked to choose between two jobs, and told that he couldn't have both. He chose one of them. Describing that as being "fired" is whack. "He was fired for choosing to work somewhere else instead of here", really?
Firing: Your boss decides that it's time for you to go.
Ultimatum: Choose between these options, or it's time for you to go.
The only part that might not be right is the tone. I think "ultimatum" sounds a bit adversarial, whereas PG is describing something more cooperative in nature.
