Use of Factory pattern — how to implement it

I am trying to figure out how Factory pattern works. I implemented it with TypeScript in this github repo: https://github.com/emilecollin/factory_pattern

Basically this is emulating spaceships gaming logic: the program will ask you to input in the terminal one of these options: "alien" or "zombie". With the provided input, the program will select on runtime the proper ship class to instantiate (AlienShip or ZombieShip), and a spaceships fight is mocked. The logic for the decision of which spaceship class to instantiate lives in a «factory method».

I'm now sure if I got it right. Still a bit confused about it. Any opinion of this code will be welcome!