I have a new non-stick pan and it's the first time in my entire life I've had this issue when frying an egg.
Whether I'm on 1/10 heat (Gas stove), 3/10, or 5/10 heat it does the same thing: It films over the skin of the egg with a strange texture, but doesn't actually stick to the pan.
In that video I managed to separate the film from the egg, but I'm wondering what I'm doing wrong to have that film develop in the first place? It's a firm-plastic texture, like a tupperware lid.
You've got some good suggestions here but also, consider ditching nonstick stuff for something safer like cast iron or stainless steel: There's all sorts of nasty shit used in the creation of nonstick surfaces and they can come off if the coating is ever damaged (which can be very easy to do).