Two phonological rules apply:
Turkish is fundamentally Subject-Object-Verb (S-O-V), and locative/temporal phrases often sit right before the verb. In our example:
• Subject = kedi
• Location phrase = arka kapıda
• Verb = gizleniyor
You could shift arka kapıda for emphasis, but the verb usually stays at the end.
It breaks down into:
• Root gizle (“to hide”)
• Middle/passive suffix -n, turning it roughly into “hide oneself”
• Present-continuous tense suffix -iyor
• (No extra ending) because third-person singular doesn’t require a separate suffix in this tense
So gizle + n + iyor = gizleniyor (“is hiding [itself]”).
• gizlemek is a transitive verb: “to hide (something/someone).” You’d say “he hides the treasure” as hazineyi gizler.
• gizlenmek is the middle/passive form: “to hide oneself” or “to be hidden.”
Since the cat is hiding itself (not hiding something else), we use gizlenmek, yielding gizleniyor.