I think people are looking too deeply into "the game warden". It's likely just one of the multiple clones (the one that prevented him from skinning the buffalo) Veidt engineered and probably gave the directive to watch over him/his actions. Veidt's "exile" seems more self-imposed than anything else.
in this episode there were multiple clues towards genetic engineering (besides them being clones). he told one of the clones "you are not capable of feeling doubt, but i appreciate the sentiment", and then after that one froze to death in that experiment he told the other one "we will need a thicker skin", and immediately after he went hunting for a buffalo's hide.
this suggests he can add/remove traits to his clones at will. it would not be far-fetched he would have created one with the sole purpose of existing as some sort of guard/warden that watches over his actions, as a reminder or as to not allow him to break his exile.