I would imagine Gilberts role as "QB Coach" has more to do with the mental side of running this offense regarding reads, protections, audibles etc. King will likely still play a large role in working with QF in terms of physical fundamentals. RB coach is generally regarded as the easier of the position coaches, leaving him plenty of time pre/post practice to work with QF while installing the run game.
Keeping King was huge for various reasons, but for me the biggest thing outside of what's already been mentioned is having a guy that's well respected with a high football IQ who watched this offense ran effectively this season. I'd imagine Gilbert will be bouncing ideas off him about what worked and didn't work last year.