To be pedantic, the rules, as you say, dictate that "the (black) mercenaries surround the King". In the game in question the King moved into the position where it was surrounded by black pieces (plus centre) but the word "surround" indicates positive action on the part of black which clearly did not happen on the immediately preceeding move.
This is similar to a white (for instance) piece being placed between two black pieces. In this case the white piece is not removed from the board because neither black piece put it into that situation. If this is the case the rules in both circumstances are consistent.
It is interesting to note that had black not captured the last white soldier a win would eventually have been possible and the white piece would not have been able to capture any more black pieces (as the King cannot be used in the capturing move - a clarification which should probably be added to the rules).
(gem) Hvis du venter på din tur kan du klikke på "ændre" ved siden af "Opdater" på hovedsiden, sætte "Automatisk opdaterings-interval på hovedsiden og spilsiderne" til 30 sekunder. Så får du vist din tur hurtigere. (Servant) (vis alle tips)