The Mayflower Compact establishes a form of TEMPORARY government based on the Social Contract theories of John Locke. The Pilgrims aboard the Mayflower were not declaring their independence from King James, they were merely stating that they had a new government until a better and more stable government could be established. The Social Contract Theory is a theory written by John Locke theorizing that the power/authority/legitimacy of a leader exists in the will of the people, and the people give their leader consent to govern them/give them protection, etc. But if a leader misuses/abuses that power, the people can take away their consent and give it to another leader.
I hope this helps!