You have two different parts of speech here, an adjective and a noun.
In "the kingdom walls", kingdom is an adjective (more specifically a noun adjunct, a noun being used like an adjective to modify another noun. See here for further discussion of the concept). So a "kingdom wall" would be a special type of wall. Similar constructions would be "mud wall," "stone wall," "outside wall," etc.
In "the kingdom's walls", kingdom is a noun, in the possessive case. "A kingdom's wall" is a wall that belongs to the kingdom, or is in that kingdom.
The difference can sometimes be too subtle to distinguish between the two. For example, there is little difference between "I demolished the bedroom walls" vs "I demolished the bedroom's walls." But in the case of a kingdom, "kingdom walls" would only work if there were multiple walls that were specifically around the whole kingdom. If you're talking about multiple city walls within a kingdom, you should say "kingdom's walls".
As for The God Virus, this is one of those cases where the distinction is very clear. The author didn't mean a virus that belongs to God, or was created by God, or is transmitted by God. In fact, he doesn't seem to believe in God. What he means is that the idea of God is like a virus, because it appears to propagate itself. So he used "God" as an adjective to describe the virus.
Here is another example to illustrate the difference: "picture frame". If I say "I want this picture frame", I might be referring to a frame sold separately in a store. If I say "I want this picture's frame" I can only mean a frame that already has a picture in it.
Another example is "the glass vase": here "glass" describes the vase, and it's immediately obvious that it can't be phrased as a possessive. "The glass's vase" makes no sense.