While watching this episode, why did Tzim-Sha wait to take Earth? one of the planets was taken by Paltraki and his crew but this didn't have any effect in the acquisition of Earth later in the episode. There was no point for Tzim-Sha to re-acquire the stolen planet from Paltraki, as he could have just taken Earth before the Doctor arrived.
He wanted to show the doctor what he was going to do out of jealousy and anger for the doctor sending him across the universe all those many years ago also he hoped when the doctor showed up she would not be able to handle seeing earth be destroyed and help him return back to his home planet while possibly killing the doctor in the process, (not knowing the doctors ambiguous mindset able to do multiple tasks through her/his time lord intelligence and years of experience and bravery and capabilities of dealing with all sorts of hostile raced aliens, including earth, and countless other planets of people who would do the doctor harm).
We know that Tzim-Sha was essentially a trophy hunter. He wasn't originally driven by revenge as his targets were selected at random.
"Our leaders randomly designate a selected human. I'm sent here, alone, no weapons, no assistance. I must locate and obtain the trophy and return home with it, victorious."
-The Woman Who Fell To Earth
But as Tzim-Sha went on to explain in The Battle of Ranskoor Av Kolos:
"The Stenza held people in stasis as trophies, but that was never the goal. Our ultimate goal was to hold civilisations."
The planets that he had collected were trophies, perhaps ones originally selected by the Stenza, and not based on his own desire for revenge.
Although he certainly did target Earth as a form of revenge upon The Doctor, this was incidental due to her arrival on the planet and the fact that he could make her watch him do it. Tzim-Sha knew that The Doctor was not from Earth and could not have exacted revenge upon her by simply going after Earth at any time when she might not even have been on it.