Can the aforementioned Hadith be considered a direct proof of the prohibition of masturbation and what falls under its ruling?

The hadith is not considered evidence for the prohibition of masturbation, because those who deem it permissible do not consider it among the forbidden acts by Allah, and for those who deem it forbidden, the hadith contains no evidence for its prohibition. Rather, it may be included among the forbidden acts by Allah based on other evidence. The hadith is mentioned to remind that whoever commits forbidden acts is exposed to punishment. This does not mean that masturbation is permissible; rather, it is forbidden and harmful.