king of cups
For me, the king of cups is fire/wands expressing themselves as water/cups.
In a positive sense, when his wand nature and emotional style of expression are balanced, the king of cups is a man who knows how to party and enjoy life to the fullest, a true epicurean. He has a rich emotional life and can live and express this adequately, this also teaches him compassion and empathy for others. This makes him a good father, lover or friend, but he never forgets his wand nature and also knows how to look after himself. He is deep without loosing himself.
In a negative sense, the wand nature is weak and the flow of emotions sweeps him wherever it would. Such a king of cups can be a drunkard or addict, depressed or generally a weak man who is overwhelmed by his emotions.
If the wand nature is disturbed rather than just weak, he lives self-destructive emotions and urges with all the power and determination of his wand nature.
When his wand nature (fire as sheer power and drive) is dominating his cups style, he can be a manipulative person who uses the expression of emotions to their own ends, in good or bad ways. He is not living emotions but (ab)using them.
Like you would expect from a dark deck, the Archaeon Tarot emphasizes the bad aspects, especially the first one. The picture shows (at least for me, it's somewhat hazy) an overweight, somewhat effeminate man. He looks as if he is brooding on the sorrows of his life. He looks away from his cup and from the obvious skulls, a sign that he is not handling things very productively at the moment.
In the corner where he's looking, you see a little skeleton looking in his direction. He is refusing to confront the sorrows and upheavals at hand only to be confronted with a ghost of it all that very well might be worse. As others already have observed, half of his face is in the shadow, he is not fully living his potential.
In actual readings, it came up repeatedly pointing to a weak person who is preoccupied with the ghosts of his past.
In actual readings, he can mean persons of any age or gender with those qualities, or those qualities in a more abstract context.
Of course, he can probably also mean the positive aspects of the card, same as say the rws image can mean the negative ones.