The zombies did not have to think much about taking over the other continents. According to the zombies, they were the most superior race in the entire world. And for that reason, if they faced the other races, they would definitely be able to eliminate them with quite ease.
In the world that they originated from, they were the dominant race in that world. In fact, it could be said that they were the only race within that world, eliminating animals such as insects.
Nevertheless, for them to be able to dominate an entire world, it was clear that they had to clear out all the other races within that world. It might be true that within that world, the number of races within it could not compare with the races that could be found within this one, but even then, the power of those races was definitely higher as compared to the one that was here.