Whose weird cat is this on my fire escape?

We sleep with the window open, and our cat sometimes goes out on the fire escape. It is an inside cat, though, and has never interfaced with another cat IRL since we got it. This morning we woke up and our cat was outside with another cat. The other cat seemed to have come down from the direction of the fire escape above ours. The other cat was mewing towards our cat, and our cat was hissing at it. My wife was very alarmed. "Whose cat is that?" she was saying. After a while we decided I should rescue our cat. I grabbed our cat through the window and the other cat made an attempt to follow our cat into our apartment. My wife jumped off the bed and retreated into the adjacent room screaming "Oh My God". I shut the window half over the back of the weird cat, and it retreated outside but did not leave our fire escape. Thereafter a weird cat showdown occurred as documented in this video:



This kind of window attack recurred five or six times over the course of ~ 20 minutes. After this, the weird cat perched atop the outside of our air conditioner. Looking at the weird cat, which atop the air conditioner seemed to be floating in empty space, eerily satisfied with itself and the uproar it had created, we discussed some theories about the origin: 1) Had our upstairs neighbors taken in a cat without letting us know? This seemed unlikely, as they already have a dog. 2) Had the cat come from the long corridor of "courtyards" behind our apartment? It seemed it must have. But then how did it get up onto our fire escape? Could it have climbed a ladder? 3) Was the cat a stray? If so why was the cat’s long hair not knotty and dread-like? 4) Was it a woman cat in heat? These questions and more continue to intrigue me as I write this. I hope the weird cat comes again tomorrow. UPDATE: The cat returned and we let it inside. Then I removed it because we were unsure if it had fleas.