It is an observational study, meaning it cannot assign cause and effect. That's not a slam against this study- it's just a statement about experimental design and what conclusions you can logically draw. When you don't know much about a phenomenon an observational study is the way to go so you can hoover up as much data as possible.
In this case, it looks like they've hoovered up some good stuff! They used objective measures- all that serum biochemistry and urine samples to measure- to describe PEM. These measured changes also align with other research that's been done on ME/CFS suggesting there's replicability going on. A good sign in research that you've found a real effect! ME/CFS patients were identified using Canadian guidelines (not Fukuda!) so we think that they really had ME/CFS. I would like to see more demographic info on the participants. They mentioned they gave a depression questionnaire, but I couldn't find anywhere those results were included. Maybe I missed that though-brain issues, you know.