It's clearly not romantic, just a respectful goodbye kiss on the hand. As you can see, the man's head is positioned far from the prince's face, maintaining clear distance. There's absolutely nothing in the image or Manhwa that suggests or implies anything inappropriate from him, let alone pedophilia.
There’s absolutely nothing from his side that suggests he ever had romantic feelings towards the kid. If he’d truly felt that way, he would’ve come back on his own instead of waiting years to be called. Whatever “romance” people want to imagine was completely one sided. Please stop. The story is painful enough; don’t twist it into something it never was.
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Blushing does not reliably imply romantic attraction.
Blushing is primarily a physiological response driven by the sympathetic nervous system, adrenaline causes blood vessels in the face to dilate, making the skin turn red. It happens in many situations that have nothing to do with romance. His blushing occurred because he was embarrassed and shameful for not keeping his promise. The position of the Prince’s head is further away from him.

But, am I wrong or did Sam actually have some romantic feelings for the king, because he kissed him before he left him??
I mean we don't see the nature of the kiss but..
Also he goes on about wanting to be the sole important person in the kings life before leaving soooo.... am I the only one who thinks this? or came to this conclusion?