No, the opposite. Some might 'hope' that you could represent everything in QM with simpler Real numbers, and avoid Complex numbers (or equivalent formulations that include rotation symmetries, as other commenters point out). But the title and article claim that any such hope is falsifiably dashed. Now, the use of Complex numbers to represent QM is basically standard for like half a century, so this result is more along the lines of "things we figured were true for a while because the math just works out so much better this way but we weren't certain enough to call it for sure until now".
Actually, despite the title, the claim in the paper is that real-only-QM could be falsified, not that it has been. As far as I can tell, no one has actually done the experiment to check. Logically, it's just as possible that complex-QM could fall. There's a certain amount of hubris in seeing a case where there are two theories that agree in all known cases except one we haven't checked, and assuming "Well that must mean the one we thought of first is right!"
> real-only-QM could be falsified, not that it has been
Thanks for the clarification!
No, it means that quantum mechanics is correct, and that you cannot get around the fact that it needs complex numbers. The complex numbers represent what is really going on in the universe better and more accurately than simple ordinary non–complex numbers do.
It might mean that complex numbers (real plus imaginary part) are real in the physical sense.