I'm a doctor working in Kuwait where non-Kuwaitis should pay for health services. Some of them can't pay. Is it right to offer them the service without paying despite that it's not allowed by rules?

Praise be to Allah, the Lord of the World; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
If your contract with this hospital stipulates that you should not treat foreigners except if they pay a given amount as fees, then you should comply with the clauses of the contract as you are but an employee and have no right to act as an owner.
But it is recommended for you to help all Muslim patients outside your working hours and Allah will reward you for that, Insha Allah. Such an act is considered as relieving the pain and distress of a Muslim and the Prophet said: "One who fulfils the need of another Muslim, Allah will fulfil the former's need. One who removes the difficulty of a Muslim, Allah will remove one of his troubles on the Day of Judgement. Similarly, one who covers the faults of another Muslim, Allah will cover the former's faults on the Day of Judgement". [Reported by Imam Muslim]
Allah knows best.