Dugin has no power or influence on the Russian elite. Only clueless westerners post links to this book. Putin's imperialism is of his own biographical origins, and there is no shortage of other nationalist/pro-imperialist authors. Dugin is just one of the more intellectual ones, which isn't actually helpful in getting him popular among the Putin's "elite".
Whether it was influential or merely representative of a Eurasianist Russian Idea, the book has been prescient as a guideline for over 23 years. I wouldn’t expect it to be directly held contemporary doctrine. After all, the world is a bit different than it was back then.
This does not rely on any current influence by Dugin, who did not write the book entirely on his own.