Not a cat person, but I've worked with raptors. Staring at them tends to mean "I intend to eat / fight you". I understand this to be true of lots of mammals as

Not a cat person, but I've worked with raptors. Staring at them tends to mean "I intend to eat / fight you". I understand this to be true of lots of mammals as well (e.g. you should avoid making eye contact with wild bears that you encounter). I can therefore interpret the slow blink as 'defusing' the aggressiveness / threat of a direct stare.