Have you read the footnotes? There are several papers referenced. From an evidence based medicine standpoint this recommendation is rather weak but the benefits appear to outweigh the minimal cost and risks.

No, I did not read the footnotes in the longer 49 page pdf in your link, I only scanned the 2 page summary. In the Pre and Postexposure Prophylaxis (The I-MASK+ protocol) section, page 11:

> Melatonin (slow release): Begin with 0.3 mg and increase as tolerated to 2 mg at night. [1,7,69-75]. Melatonin has anti-inflammatory, antioxidant, immunomodulating and metabolic effects that are likely important in the mitigation of COVID-19 disease. It is intriguing to recognize that bats, the natural reservoir of coronavirus, have exceptionally high levels of melatonin, which may protect these animals from developing symptomatic disease. [76]

For the more serious stages:

> Melatonin 10 mg at night (the optimal dose is unknown) [75]

From my quick scan of the papers in the related footnotes, melatonin is a good antioxidant and may be anti-inflammatory, in addition to the well known association with sleep regulation.