It can be hard to tell through the popular science stories, where the author is typically unable to relay anything about this research without adding "woo woo" sounds and wiggling their fingers, but it's a real theory.
One thing that may be worth remembering is that in the real theory, the "simulation" is not necessarily running on "a supercomputer just like what we have, only way bigger", which is actually a silly idea for various reasons, and we also do not know that the simulation is literally simulating every particle and every cubic inch of space in the most accurate possible way (i.e., for all we know, far away galaxies could just be a few megabytes in size, rather than fully simulated to the nth degree). The "Great Simulator" is not required to run anything remotely resembling our physics. What seems an absurdly large computation may be smaller than it appears, and may not be an absurdly large amount of a universe running on fundamentally different physics.
(Occasionally when I'm bored, I noodle around with a theory of cellular automata in which the universe has infinite computation power by virtue of being able to split a cell in half or quarters, that then runs at double-speed relative to the outside. If this is done recursively the universe has arbitrary computation abilities relative to the "top level". I've never worked it into anything usable, but I think it can give a flavor of why we should not be sure that our simulation host is necessarily as staggered by the computation as we would be. We are not even capable of saying that they aren't running an exponentially-expensive quantum approximation algorithm with the entire universe actually arbitrary-precision integers under the hood. The staggering amount of computation that represents may not bother them at all.)
It is not a theory that is, strictly speaking, falsifiable thanks to Church-Turing equivalence, but there are ways in which it could potentially (to any arbitrary degree of confidence you may want) be confirmed if it is true. To take one degenerate case, if the Great Simulator broke silence and starting wildly breaking the laws of physics to get our attention, that would certainly put a lot of probability mass on the "we're a simulation" theory. There are less extreme cases we could conceivably pick up on, that just fits into an HN comment nicely.