Snakes aren't always active animals. They are often at their most active for their first couple weeks in a new home, as they investigate their surroundings, look for escapes, and settle in to the new routine. It could be that, now that the king is settled in, it just doesn't feel the need to be active through its enclosure. Nothing new to investigate or worry about, and it's content to just settle in and relax.
It could also be the set up. "Has all the tank requirements" doesn't tell us ANYTHING about how it is set up. For all anyone knows, you're doing something VERY wrong and don't even know it that could be the key to this or some other health concern. The first thing that comes to mind, is kingsnakes are nocturnal. A light over the enclosure does not hurt, but it can entice a snake to hide much more than normal (this is not unhealthy; just a fact). One other aspect of this is that, since they are nocturnal, the snake may just not be coming out to explore until everyone has gone to bed.
Then comes temperatures... What you may be under the impression is "right" may be "wrong," that is even if you monitor it as well as you should. I believe the requirement for Cali kings is a 90*F "basking" spot. The norm to do this would be with a heat pad and a thermostat. It can be done with a heat lamp if you insist on keeping the light, though heat lamps are also extremely drying and unpredictable (what may reach 90* one day may exceed 120* the next day), and they don't accommodate a temperature gradient as easily as a heat pad.
Then there are the little things... Things like enclosure size--too big of an enclosure for a vulnerable hatchling can have it cowering under a hide lest there be predators lurking right outside. Too few hides can have the same effect. Then there's substrate. Many people make the mistake of thinking sand is okay for cali kings, where, like dragons, it can be a severe health (impaction) risk. Impaction could easily cause lethargy, among other issues.
Just some things for you to think through... Though my guess is the snake is just being... well... A snake. A paranoid hatchling snake that doesn't want to be eaten by some predator lurking overhead. Completely normal behavior for any hatchling snake.
Really, as long as the temperatures in the enclosure are right, don't worry about it. Now, if the snake stops eating or starts presenting other health concerns (i.e. regurges, diarrhea), THEN is the time to worry. For now, I don't think this lack of activity is anything more than the normal behavior of your standard kingsnake.