What is the Ruling of Praying Over the One Who Killed Himself Intentionally?

Yes. He should be prayed over, because he is a Muslim. And him killing himself is a major sin, but it doesn't take him out of Islam. He committed a major sin, and this major sin is lesser than Shirk and Kufr. So, he is considered to be deficient in Iman (Faith), and he doesn't leave Iman by killing himself. And he is treated as a Muslim, he should be washed, shrouded and prayed over. Except that the scholars mentioned that it is not befitting for the people of virtue (i.e., eminent, respectable people) and exemplarity to pray over him, for the scholars or those in authority in order to deter people from this crime. As for the general Muslims, then they pray over him and he shouldn't be left without a funeral prayer, because he is a Muslim.