This is an epidemiological study, so you have to be careful about how you interpret it. They did try to account for general dietary intake via a questionnaire, but it can be hard to get accurate data this way. I still feel that the underlying cause here is that people who want to lose fat tend to take in more artificial sweeteners, and not that artificial sweeteners cause people to put on more fat.

Epidemiological studies are usually the only thing we can go by, though, because RCTs are hard to apply in many instances.

Edit: I also should mention that epidemiological studies are useful. Just that they may require interpretation and are not usually a smoking gun by themselves.