You can use it for anything
My sister worked as a Grip for a theatre company for a while. She loved it, getting to go backstage and make sure everything worked properly for performances, chilling with the cast, and soaking up the atmosphere. She also came home with some pretty useful DIY tips, usually involving duct tape.
The motto of the Grip or stagehand seems to be that you can use duct tape for anything. If it’s broken, then duct tape will fix it. I feel as if this particular landlord might have spent time with the same group. He obviously thinks that duct tape is the perfect way to fix these tiles and make sure no more falls down. I remain skeptical.