In English, nouns can be used as adjectives: "airplane glue", that is, the glue used when making model airplanes. Nouns are said to be used attributively when they're used as adjectives.
These nouns-as-adjectives can be chained or stacked up:
model airplane glue
In technical writing such concatenation is very typical, because it is perceived to be a terse and efficient style.
The following sentence
It is important to note the distinction between a RRset's TTL value
and the signature validity period specified by the RRSIG RR covering
could be made more verbose:
It is important to note the distinction between the RRset's time-to-live ("TTL") and the period during which the signature remains valid (the "Signature Validity Period") as specified by the RRSIG RR that covers the RRset.
With respect to your question, why didn't the author use a possessive?
The noun in question is "signature". Yes, the author could have written:
... the signature's validity period