The first point to note is that the Isle of Man is not technically part of the United Kingdom. It is a Dependent territory of the Crown, and is entirely self-governing as far as internal and fiscal affairs and social policy are concerned. This makes it more independent than Wales, Scotland or Northern Ireland. It makes an annual payment to the UK for dealing with all external issues 'on its behalf.'
The internal independence is no spoof. Two major instances have been its low tax fiscal policy and its adherence to corporal punishment. The island enjoys a special relationship with the EU under a Protocol of the UK's Accession Treaty. It is neither a full nor associate member, but is bound to the EU's tariff policy. However, it does not contribute to or benefit from the EU's funds, and thus remains able to keep its independent tax policy.
Tynwald, the Isle of Man Parliament, claims to be the oldest legislature in the world in continued existence. Its Houses are the House of Keys and the Legislative Council, the first having 24 members who are elected every 5 years. The Legislative Council acts mainly as a revising chamber and has 11 members, 8 of whom are elected by the House of Keys. The other three are the Bishop, the Attorney General and the President of Tynwald who is elected by Tynwald as a whole.
The Chief Minister is chosen by Tynwald from among its own members.
Party politics, as it operates in the UK, is not relevant here and most sit as independents.