the name wasn't, nessesarily Koenig
but other than that a top german sniper WAS sent to hunt Stalingrad. as far as i could find info there isn't any direct german reference to sending anyone out after Zeitzev(sp?) specificly. but due to heightened losses amoung the german "snipers" sent into Stalingrad, an Instructor from the school of marksmanship (or whatever they called it) was sent to observe, instruct, ect. the conditions and troops in that h*!lhole.
the russians became aware of this man's presence and sent Zeitsev out to hunt him. whether or not the german "instructor" ever chose to reciprocate i do not know. but we have matching time periods for the germans deploying the "ubersniper" and zeitsev's account of the arrival of a german who the high command wanted him to find and eliminate. there is even an aproximate correlation between the cessation of reports from the German sniper to Berlin (and also his disappearence from german records period), and the date on which Zeitsev places his killing of a "german sniper of high rank" that had built a hide under a piece of scrap metal, near the train yard.
so yes the german officer represented by "koenig" is real, but the "reality" of the zeitsv/german ubersniper duel is questionable. Zeitsev's kill record is legit, his killing of a german officer of the sniper corps is legit. but no one knows if the officer in question was sent to "kill zeitsev", for all we know he could have been there to simply gather data for how to better use Snipers in such an enviroment. but the Russians made it a great personal duel, for propaganda purposes regardless of whether it was legit or not.