Does ruqya work for non-practising or non-Muslims?

Healing comes from Allah, and He gives it to whom He wills. The recitation is not a reward for piety, so ruqya can and does benefit people who pray irregularly or not at all, and people outside Islam.

That said, practice makes a visible difference. Someone maintaining their prayers, guarding their tongue, and reciting daily gives the treatment far more to work with, and tends to recover faster and relapse less.

How to handle it with patients

Encourage repentance and prayer warmly, because they benefit the person regardless of any illness. But never make treatment conditional on it. Do not tell someone they will only be cured if they pray. That is emotional leverage, and it is not yours to apply.

Treat the person in front of you. Teach them what helps. Leave the outcome to Allah.