In this case you could use the singular to express that generic meaning in Greek, but you'd do so without an article: γάλα αγελάδας rather than γάλα της αγελάδας.
From a quick google, it does seem like γάλα αγελάδας is the most common way to express the generic concept of milk that comes from cows, and less frequently you see γάλα των αγελάδων.
Well, from that perspective "Το γάλα αγελάδας/Το αγελαδινό γάλα..." would be equally correct for a general approach. However, the version with the article is not incorrect. One could be talking about a specific cow, without using αυτή/εκείνη.
Το τρίχωμα της γάτας είναι μαύρο. - The cat's fur is black.
Ο σκύλος έχει μικρά αυτιά - The dog has small ears.
The article is there, yet not all cats have back fur and not all dogs have small (short) ears. These cases are not necessarily general, so this one might not be either. It could be, but it's not something too obvious, so it doesn't need to be.
So, since there is that ambiguity, both versions (with and without the article) are included in the English translations. ^.^