I have never seen the series, but it sounds like it is closer to the novels than the 1984 movie ever was. The movie did not stick very closely to the original novel at all.
However he does have extraordinary abilities and training. As described in the novels:
Due to his genetic heritage and the spice he is consuming, he is prescient. I would not go as far as saying he is omniscient, but he can look into the immediate future and see events happening far away from him on other planets. In Dune Messiah, for example, the conspirators take measures to hide their conversations from this ability.
He has had an incredible upbringing as the heir to a Major House, with the finest tutors - schooled in literature, music, diplomacy, politics, tactics and fighting skills in particular. He is designed to be the perfect leader of a Major House - a ruler of a planet in a time where political assassinations and war seem common.
He has had Bene Gesserit training, so has an uncommon understanding of his own physiology and psychology - able to control his body in a way that normal people cannot. By reading subtle signs he can also tell what people are thinking and whether they are lying. He is also able to control them for very short periods through voice commands using a skill the BG call "the Voice".
As a result of his fighting and Bene Gesserit skills, coupled with his growing prescience, he is able to fight and best anyone in one-to-one combat.
The Bene Gesserit also seeded particularly rough planets like Arrakis with legends that a Bene Gesserit visiting the planet could take advantage of. Paul and Jessica use these legends explicitly to gain an advantage on Arrakis. As a result the Fremen accord him the status of the ultimate leader to unite the different clans.
So Paul was not 'god like', but had specific advantages over others around him that enabled him to manipulate an entire culture (the Fremen) to rally to his cause.
Coupled with his training in fighting skills and tactics, the Fremen rise to be the dominant fighting force in the galaxy, exceeding the Emperors Sardaukar. Coupled with his complete control over the spice, this is the reason he rises to be Emperor - not some mysterious godlike powers.