Cat Staring Contest [Video]
These two cats seem to be locked in a battle to the death. Maybe the death is a little extreme, they are staring at each other. Cats will do that. They like to just glare at other cats, people, dogs, plants and other stuff.
I would guess these two cats are trying to determine superiority. Who is the alpha cat? I would think it's the cat that doesn't blink first. Or maybe its the cat that knocks the other cat off the ledge. That would work too.