First, Kings Gun Sight company (not Kings Armory) did not engrave guns, AFAIK. I never heard of them engraving a gun. They customized the guns but not in that way. They commonly replaced hammers and front sights, and added barrel ribs, etc. King modified guns are fairly scarce today.
While the engraving may not look factory, no one here can say that for sure. I doubt any of us have any true factory engraved guns, and of course, you would have to compare guns from that period, to analyze the engraving. The gun is a post war K frame, likely a K-38, and if the hammer is original (its a speed hammer aka fish hook hammer), its likely a 5 screw as well, so you would have to compare it to post war engraved S&Ws. Alvin White and Russell Smith were two of S&Ws more famous post war engravers.
The target grips or lack thereof have nothing to do with the lack of engraving pattern near the grips. The person who ordered the engraving would have specified which type of grips. Since the grips were removable, there was no point in accommodating the grip type with the engraving UNLESS the engraving was ordered that way. I have saw many engraved 44 mags, which never had magnas as standard, have the inner aspect (which was covered by target grips) engraved. The owner then just put on magnas to show the engraving.