This music is definitely a part of Russian culture but I wouldn't call it "typical" music.
The thing is that modern music here in Russia doesn't sound anything like the pieces you posted.
Those you posted are good examples of "music of 80's"; nowadays music here sounds like:
NYUSHA / НЮША - Только... (Official clip) HD - YouTube
Бьянка - Я не отступлю (Official video) - Премьера клипа на WOW TV - YouTube
МакSим - Д
Ярослава - Это любовь - YouTube
Жасмин - Нет, не надо - YouTube
These are what average Russian modern music sounds like.
Of course sometimes you can run into a brilliant in this stinking bunch of modern Russian pop-music but it's quite an occasion, you know...