Even supposing the Thing didn't create the flying saucer it landed in, it has the ability to create a new one, so there could be Things all over the universe.
Well, the common theory is that Things get smarter mostly by assimilating knowledge from their victims, and Word of God is that the 2011 film was originally supposed to prove that the Thing was picked up as a biological specimen by an entirely different alien race. So, only the Things descended from the first Thing to crash on Earth would know how to build spacecraft; it's equally as likely that "Thingworld" has been quarantined — or sterilized — to avoid just such an outbreak.
The implication I got was that this thing was a virus spreading across the entire universe.
Luckily, since the last thing arrived 100,000 years ago, they're probably dead, at least near earth.