It's cute how you added those comments with spoilers because

• Everyone watching this video has already seen Shelter, if they haven't... GO WATCH IT ^{and New Game}

• It's a theory, so not really spoilers to anything. We see a few things that help us see that the events in Shelter might still take place on Earth. When the father is watching the news for the first time in the TV, it tells us that they are watching Tokyo's current situation. Also, we see cherry blossom trees, a picture of the mom with Japanese style clothing, and a shrine(or a temple, I'm pretty sure it's a shrine). I don't know much about terraforming a planet or a moon, but when you start over, I'm guessing people would want things to change and share their culture diversity with each other. Why would they rebuild Japan as it was on Earth and not make a central cultural belief. Unless the Japanese were the only ones with the technology to terraform and decided that they were the only ones that deserved to live on one of Jupiter's moons. Is there a Jupiter moon with the name Mirai? I can't google these details for myself since I'm spacephobic.

I'm pretty sure scientists and astronomers would know if interplanetary collision would happen in the future with a planet and/or its moons and prepare an escape plan in case that would happen or not inhabit the place at all. Unless it was a totally unexpected event for the end of their planet/moon, it would make perfect sense if it was on Earth.