This has nothing to do with the genitive. It is just an example of the general principle that when you take a grammatical sentence and replace one part of speech by an equivalent one, you normally get another grammatical sentence. This is true in German to a greater extent than it is in English. Let's start with a simplified form of the subject of your example sentence:
Der Text des Buches (The text of the book)
As you know, you may add an adjective to the noun Buch, which then ends up between the definite article and the noun. (Technically, in German, participles are generally not considered to be adjectives; they just behave like adjectives in sentences most of the time. But let's ignore that and call durchgesehen an adjective for now.) This is what we get:
Der Text des durchgesehenen Buches (The text of the revised book)
This is because a noun may be replaced by a noun qualified by an adjective (or participle). As you already know, you may add an adverb in front of the participle durchgesehen:
Der Text des neu durchgesehenen Buches (The text of the newly revised book)
This is because an adjective may be replaced by an adjective qualified by an adverb. But there are also other, more complicated ways of qualifying an adjective. In particular, since the 'adjective' durchgesehen is actually the past participle of the transitive verb (etwas) durchsehen, one way to qualify it is to supply the subject of the verb, i.e. the person who did the revising. We do this by using one of the prepositions von and durch, which in this connection correspond to English by. (The choice between the two is basically free, although often one of them is preferred because the other would be ambiguous.) Thus we get the following:
Der Text des vom Verfasser durchgesehenen Buches (The text of the book revised by the author)
As you can see, German follows the general principle that qualifications to an adjective appear before the adjective. In English, they sometimes occur before (like newly), and sometimes after the adjective (like by the author).
Note: In this case this results in an ambiguity that is present only in the English version: Is it the book that was revised by the author, or is it only the text? If an important error in the cover was fixed, the difference may be important to the author. But I am sure one can also find examples where the German system results in ambiguity that doesn't arise in English.
Since a qualified adjective behaves very much like an adjective, we can also qualify it again. Thus we can qualify neu durchgesehenes Buch by vom Verfasser:
Der Text des vom Verfasser neu durchgesehenen Buches (The text of the book newly revised by the author)
Or we can qualify vom Verfasser durchgesehenes Buch by neu:
Der Text des neu vom Verfasser durchgesehenen Buches (The text of the book newly revised by the author)
Here we see one aspect in which German grammar genuinely creates less ambiguity. If you add some qualifications before a word and some after it, you will never be able to clarify the hierarchy between them through their order. This is why the last two English translations are identical even though the German sentences express slightly different ideas. The version vom Verfasser neu durchgesehen just implies that someone revised the book, and that it was the author who did it. In the version neu vom Verfasser durchgesehen, however, neu (newly) would qualify the entire phrase vom Verfasser durchgesehen and therefore would imply that the author has done it at least once before.
(Note that the following slight difference in meaning between durchsehen and revise becomes relevant here. While durchsehen literally translates to look through (or peruse), revise has a strong implication of looking at something again. Therefore one is more likely to include editorial work done before the first publication in durchsehen than one is to include it in revise. Consequently, the most likely meaning of neu vom Verfasser durchgesehen is that the author did this work him-/herself for the first edition and has now done it again. There is no suggestion that we are talking about at least the third edition and that the author has already done another post-publication revision before.)
It is also possible to combine two qualifications of an adjective using und:
Der Text des übersetzten und durchgesehenen Buches (The text of the translated and revised book)
This also applies to more complicated qualifications:
Der Text des von Kesting übersetzten und vom Verfasser durchgesehenen Buches (The text of the book translated by Kesting and revised by the author)
Or even more complicated qualifications:
Der Text des von Dr. H. Kesting übersetzten und vom Verfasser neu durchgesehenen Buches (The text of the book translated by Dr H. Kesting and newly revised by the author)
With almost no bounds on how complicated the qualifications may get:
Der Text des mit der von ihm gewohnten Sorgfalt durch Dr. H. Kesting übersetzten und trotz widriger Umstände vom Verfasser neu durchgesehenen Buches ... (Literal translation: "The text of the - with the for him usual accuracy - by Dr H. Kesting translated, and - despite adverse conditions - by the author newly revised, book ..."; proper translation: "The book was translated by Dr H. Kesting with his usual accuracy and newly revised by the author despite adverse conditions. The text of the book ...")
This is an example of a typical problem that arises when translating from German to English. Just as in translations from Latin, you very often have to split a long German sentence into several shorter English sentences. (In this last example I replaced "von Dr. H. Kesting" by "durch Dr. H. Kesting" because this prevents the sequence of words "Sorgfalt von", which is not a phrase but could erroneously be taken for one, leading to a failure to parse the sentence correctly.)
