No.
As far as I'm concerned, you can only omit it for something you only have one (country, body parts, etc) or for people (e.g. father, teacher, friend, etc). Book isn't one.
In the English sentence, one nuance of it is "They are going to publish their book, not the speaker's (or the hearer's) own", not as stressed at the possessive word "của" as in the Vietnamese sentence one. But still, it is not possible to leave the word "của" out.
Is the audio missing a word? I understand the accent is southern and the course is predominantly northern, so my ears have become adjusted to the north, but doesn't sound like gio before ruoi is in there.