“Laysa” is a defective verb whose subject is nominative and predicate is accusative; its predicate may precede its subject. In the reconstructed “لَيْسَ مِثْلَهُ شَيْءٌ”, “mithlahu” is the fronted accusative predicate and “shayʾun” is the delayed nominative subject.
In the expressed “لَيْسَ كَمِثْلِهِ شَيْءٌ”, kāf is a preposition, “mithlihi” is genitive in form, and the prepositional phrase occupies the predicate position. “Shayʾun” remains the nominative subject of “laysa.”
This requires distinguishing the case marked on the noun itself from the syntactic function of the entire prepositional phrase.