Political system doesn't mean only Electing a head of state or head of govt. eg . In England , firstly PM were elected by the wishes n whims of Monarch, eg Pitt the younger, lord north.
Then system changed to party strength in parliament... And now they are elected from majority party.
The parliament (the MPs) were initially elected by landlord genetry, then by capitalistic class as well, then proleteriat gained enfranchisement, and eventually through universal suffrage. Now this system changed over a period of time , wil we say England has no political system? Certainly we wont.
Political system is more concerned about the portfolioes, rights, obligations and accountability of the leader... Islam has clear and discrete principles n injunctions about them. However the process of election is amenable to evolve, systems evolve over a period of time. During Rashidum caliphate , common men were ignorant. If they had been given the right to elect their caliph they would have done hovac to islam. So islam had to adopt timocracy... The advisory council was elected on the basis of piety. Now this process of election can be modified, but code of conduct that is the heart of political system wil remain the same.