Yep.
Is it common for a player to become rusty if he does't play for a long time?
Yes, generally it is. And a long layoff from chess would affect not only your creativity but also your style. I am always an aggressive player, always thinking of attack even if the position doesn't demand for such treatment. Once i stopped playing chess for a few months. When i come back to active play i noticed that i became too cautios in my games. In a way having not played for a long time actually taught me something about defence!

i did experience it....once i returned to it after a month, it dropped to around 1100...then i have this feeling that i should rather play those rated 800 in order to win...
Any skill requires regular practice just to maintain it at the level currently possessed. Without practice the skill will start to decay...

Is it common for a player to become rusty if he does't play for a long time?
No, not at all. In fact usually people get better the longer they don't do something. This isn't just in chess, but everything.
It is probably true for the vast majority of players but there are exceptions. Emmanuel Lasker stated that he "gave up tournament chess for two periods of six and seventeen years, packing all books in boxes tightly taped shut, sequestered in the attic."
http://chessimprover.com/emanuel-lasker-on-chess-improvement/
Despite Lasker's periods of turning his attention to other matters he would always come back and play at the level of the world's strongest players. I never followed the games Bobby Fischer played in 1992 but have read numerous articles on how the games he played 20 years after winning the title were at a very high level. Of courses these were gifted players and no doubt the exception.

It is probably true for the vast majority of players but there are exceptions. Emmanuel Lasker stated that he "gave up tournament chess for two periods of six and seventeen years, packing all books in boxes tightly taped shut, sequestered in the attic."
http://chessimprover.com/emanuel-lasker-on-chess-improvement/
Despite Lasker's periods of turning his attention to other matters he would always come back and play at the level of the world's strongest players. I never followed the games Bobby Fischer played in 1992 but have read numerous articles on how the games he played 20 years after winning the title were at a very high level. Of courses these were gifted players and no doubt the exception.
"World's strongest players" in Lasker's time were not pros so... this is just Lasker being amazing. Surely past his peak if he had stopped practicing and thinking about chess.
Kasparov estimated 90s Fischer to be in the 2500s

No, not at all. In fact usually people get better the longer they don't do something. This isn't just in chess, but everything.
Though I realise that this is in jest, I do find if I leave chess for a day or two, or a week or two maybe, I often play better when I return.
I also had a gap of 35 years at one point, and was back to the same standard (not awfully good admittedly) within a few weeks.
6 months ago i was a 1500 rated player. Then i stopped playing chess and now i can't defeat even 1200 rated player. Is it a common problem? :(