There are two variations in my experience... of three years searching for the perfect king kong parrot. There are so called "asian" standard kkp, which CAN have a triangle mouth, though the upper lip is not deformed. this results in a mouth that is open on the bottom but not on the top. these fish will have a sloped forehead and can produce nuchal hump. This variation is asian standard and I call this because it is the description on the happy breed website, who i consider an authority as they make mammons. the other qualification for this type is that the anal fin is longer than the tail. There are many ways to make this as it is an intermediate form between the blood parrot and mammon/ingot, but this form usually has more syns blood.
The other form I call the "american" king kong parrot or the mini-midas. These are made usually in america by breeders intending to produce viable blood parrots from lines without much genetic diversity. The usual formula for these are from fertile male bpxmidas or rd hybrid or just by crossing bp with midas. This form can close the mouth all the way and has no notch and can produce nuchal hump. I am currently working on an american strain of this fish, which is essentially an SB midas.
There are many ways to get king kong parrot, but the general consensus i have come across is that the qualifying factors are that they DO NOT have a parrot "notch" in the forehead and have less of mouth deformity or perfect fish mouths. These two forms are not the only kinds of king kong parrots but are the most common in my experience. Another common trait of the KKP is that a larger percentage of them can grow over 2kg in size. THis trait is nearly 90% for the mammon and about 10% for blood parrot.
They are an intermediate breed so there is no clear definiton, but essentially kkp occupy the midpoint between the blood parrot on the low end (which can result from an F1 or F2 cross) and the mammon on the other end, which is very valuable because it is the result of decades of dilligent breeding.