The music in the first post is for people of certain age and cultural preferences. It was more popular in past decades. Antonio's examples are closer to modern definition of "typical" Russian pop music.

UPD: Now I think I see what OP means. Modern Russian pop music is quite generic Western-like pop music, while Russian Chanson & Estrade genres from the first post is definitely more distinctive and unique for Russia. They probably have highest "popularity : Russian uniqueness" ratio among other popular genres in Russia.
http://en.wikipedia.org/wiki/Russian_chanson