These websites really like to oversell research. I skimmed the paper (not the article about the paper), and essentially what they did is get blood from a cohort of people diagnosed as having ME/CFS, and it compared to a healthy cohort. They did a whole bunch of science on the samples to pick out some differences between the two groups. They then classified a separate group of people not used in training to get the model's specificity and sensitivity, and those are the reported numbers.
Importantly, there weren't people with other potential health issues.
Effectively, it's like going into a room that you know is a mix of me/cfs patients and healthy people, and having to classify them. You could probably just ask each person like 5 questions, and their answers would be enough to classify them with 95% accuracy.