Y. Averbakh and N. Giorgiev are surnames with abbreviated (?) given names, the former starting with Y and the latter with N. The year in parenthesis after each name could stand for a year of birth or the year of a relevant contribution to the book.
The position given is known as a chess problem. The problem was first composed by N.Giorgiev in 1932, then re-composed by Y. Averbakh in 1984. Most chess problems have a theme, and Averbakh's re-composition uses the theme of Giorgiev's earlier work.
Averbakh took something Giorgiev did and modified it, using it as the basis for his own development.
(Parla's right. This isn't really a language question. It's a question about how people write things in the chess world. Many fields of activity have their own specialized jargon. The instructions for knitting even a simple sweater would be totally incomprehensible to non-knitters.)
Egmont is right. Averbakh modified a position composed by Grigoriev and came up with a new problem. By doing so, Averbakh is, in a sense, praising Grigoriev's earlier work. In the music world this is like Rachmaninoff composing variations on a theme of Paganini.
Since the issue has been raised, this is definitely a language question. It is a turn of phase seen in many similar contexts. (Thank you for the good context, houshdaran!)
When we have questions about medicine, law, chess, accountancy, lacemaking, horse breeding or other areas of special knowledge, we can respond within the limits of our knowledge. Frequently there is a forum member who possesses exactly the specialized knowledge required.
Thank you all for being concerned about the forum's scope, but in this case, we're fine!