teceem: I second this! Get a refurbished office chair.
I got mine free from my former workplace when they were downsizing, closing some offices. Then they just gave office chairs and shit to employees (those who weren't yet laid off).
I also bought the cheapest fake-leather "office chair" from IKEA, one that also seemed to have the "free rocking" mode that I consider vital. It certainly was cheap (I dunno, something like 20-30€ ?), but it is flimsy as hell and I think its rocking mechanism got broken, and now it doesn't rock anymore. It is now fixed to the upright position, but at least it still rotates.
So yeah I think it pays off to pay a bit more for the chair.
teceem: Why would a "gaming chair" have anything to do with gaming (except for the name)? Isn't it obvious that it's a marketing thing? What's next? Gaming shoes? A gaming fridge?
When someone mentions a "gaming chair", this is what normally pops into my mind:
https://www.youtube.com/watch?v=zAB-0P65wRo#t=10 You know, integrated joysticks on both sides and speakers near your head? "Perfect".
I recall also those fancy "gaming stations" where you could fix a desktop PC, keyboard and a big CRT tube to the same frame with the chair. They never seemed to really pick up though, I guess people found them too... odd.