Some of this may have already been said, but this is what the manga says about Pluto, the Time Gate and travelling through time. Sorry if I'm repeating anything that has already been mentioned...
The door only leads to Crystal Tokyo (30th Century). Look at the GIF that you posted. You can see Crystal Toyko on the other side.
The space in which the door is located is between time and space (fourth dimension) and is very easy to get lost here (Luna said this). Pluto later said that the fourth dimension is a void without a concept of distance or direction.
When Chibiusa took Sailor Moon, Venus and Tuxedo Kamen to the future, she told them to not let go of her hand in case they get lost.
King Endymion also said that the Gate of Time is located at the depths of the Crystal Palace.
If you look at manga pictures of Sailor Pluto, you will see a ring of keys around her waist. You need a key in order to perform the time warp (and I don't mean the dance!), and the key will lead you back to Sailor Pluto.
Letting anyone time travel is one of Sailor Pluto's taboos, so using a key to time travel is actually forbidden, but the King wanted to let Sailor Moon, Venus, Tuxedo Kamen and Chibiusa use it because it was an emergency. Pluto didn't die as a result though (even though it was a taboo).
Using one of Pluto's keys is vital in order to navigate your way through the fourth dimension, and in a later manga act, Chibiusa lost her key, and as a result got lost herself.
Sailor Pluto used her Time Staff to return the others to the time and place they originally came from (the present). Later, Tuxedo Kamen runs off (in the fourth dimension) without a key and Pluto even yelled after him, saying that he won't be able to come back.
The far reaches of the fourth dimension are a forbidden area and not even Pluto knows what is at its depths. Pluto also says that it may be possible to be pulled into another dimension in these depths (there was a storm there at the time).
So, that's what the manga says.