The idea was simple here.
While Sheva's king was still quite safe, on that side, he had a doubled pawn that was quite weak. Not only that, Johan-Sebastian Christiansen had all of his rooks staring from afar, and while it hadn't happened yet, the attack would arrive soon. So, rather than sitting helplessly on the back, it would be better for the king to move his ass quickly, evacuating himself from the danger.
This was also in line with the common strategy in the endgame phase. Once everything disappeared from the board, it was time for the king to get active, and that was when its subordinates needed it the most in the game.
