In a way it is democratic.
After the death of the prophet they had to have a new head of state, a new Caliph.
How did they do it? The majority appointed Abu Bakr. The other faction wanted Ali.
Both were more than well qualified for the job. Both were trained and tutored personally by the prophet. Both had excellent character, although each had their strength and weaknesses.
Ali was gracious and agreed that Abu Bakr was the rightful candidate. Eventually because the fourth Caliph. There are stories that some caliphs even refused the position because of the heavy responsibilities, but had to be convinced that it is duty.
This system of transfer of power to the next most qualified person and agreed by majority existed until the end of the Ottoman Caliphate. Many times, it was not the son who assumed the Caliphate.
Yes. Islam is democratic.
