Nigeria operates under a federal republican model, based on that of the United States, with influences from the British Westminster system. Like in the USA, the president is both head of state and head of government.
Nigeria's preidential system does work well, however within the context of Nigerian politics, this is highly subjective. The Nigerian President fulfils the requirements of the Constitution, but like so much in Nigerian politics is conducted against a backdrop of of high levels of corruption and prebendalism.
Nigeria is still regarded as 'democratic', though the above problems are persistent. Even so, election irregularities are not seen to be a major problem and do not compromise the overall presidential system.
Nigeria certainly hasn't reached the point of despotism or dictatorship.