From your chosen quote, it doesn't seem to indicate that fasting specifically changed things, but fasting being an "effective means for weight loss" was the bit that really mattered. I don't see anything to divorce the two - general weight loss and improvement to the FLI.

> Available evidence suggests that any form of caloric restriction may be beneficial and specific forms of IF should be tailored to the individual.

Also important to notice that once the liver is damaged it's not recommended to fast:

> Additionally, it is important we investigate the possible risks of fasting in patients with cirrhosis, which is currently not recommended.