In my humble opinion and also as backed by research and personal experience, you can definitely lose weight utilizing water-only fasting as a tool. More importantly and more specifically you can lose fat. In addition to being able to burn fat as the primary fuel source throughout a water-only fast, there will almost certainly be a fairly significant amount of temporary water and intestinal content loss, most or all of which will be added back to the individual's weight within 1-3 days of ending the fast at which point the weight will relatively stabilize.
The link provided in your post suggests that someone can lose 5 kg in a 7 day fast, which for we Americans is about 11 pounds but as i have so commonly seen, this does not take into account that almost certainly a significant portion of this overall loss will return within 1-3 days as the water levels and intestinal content stabilize.
With myself as an example, just yesterday i completed a 7 day water-only fast, the final 3 days of which were dry... and my temporary 7 day loss was 15 pounds taking me from 212 temporarily to 197. My prediction of how much enduring loss i would achieve based upon estimated maintainence metabolism that would be burned within my body, was that once my weight stabilized within 3 days i would find myself at about 5 pounds of real loss.
12 hours after breaking the fast by drinking over several hours 2 liters of a Himalayan salted broth type content, 1 liter of kombucha, an avocado, and a tablespoon of coconut oil... and with my body choosing to hold onto most of the new water content several hours later, the 15 pound loss had (as anticipated) already been reduced to an 8 pound loss, with a bit more balancing still to come.
As such and as in past 7 day fasts, i will have lost about 5 real pounds in this 7 day fast, possibly 6 pounds, but no more than this. As far as i am concerned this is fantastic, but it is not sensationalistic / "too good to be true" as would be an enduring 11 or 15 pound loss in 7 days. I am sure it is possible for some people with different variables in place (especially extremely overweight individuals and/or people with a lot of excess water retention issues which a fast would potentially resolve) to lose 10 or maybe even 15 pounds of real loss in 7 days, but if this were the case, their loss would have to exceed the 10-15 pounds initially (would perhaps initially need to be 15-25 to then stabilize at 10-15 after 3 days) because it is almost certain that just as i have personally experienced repeatedly and just as i have learned from so many others in their experiences, a substantial amount of temporary loss will return within the 3 days.
My own opinion as well is that to utilize fasting effectively as a reliable fat loss tool, it is essential to choose a reliable lifestyle of eating in between fasts which will not allow for addictive eating to run out of control especially where grains and desserts are concerned. My personal opinion and experience is that a very low carb diet which leads to nutritional ketosis works wonders in taming appetite and thus in keeping people on track.
The strategy i would thus recommend is to stabilize oneself in a very low carb ketogenic diet and combining this with daily intermittent fasting of perhaps 16/8, 18/6 or 20/4 (or even 14/10 if someone finds it difficult to exceed this).. and then periodically alternating this stable keto diet with fasts of at least 30 hours or so... or as long as one would prefer whether 36 hours, 2 days, 3 days, 5, 7, 20, 30 or 40... then back to very low carb ketogenic eating with daily intermittent 16/8 (etc) to re-stabilize.
I also very strongly advocate resistance training while feeding as an exceedingly helpful tool in reaching the desired health goals and body composition transformation.
Edit: By the way and ps, there are a rare breed of MD's who advocate for fasting including as a fat loss tool. This attached video provides one such example: https://youtu.be/7nJgHBbEgsE