I used to have one of those rockers, for the same reason. It served its purpose, but that thing was hard as a rock and really uncomfortable for my back. Those chairs arent going to make your game any better, and it was a bitch to cart it around as it didnt fit under any table or neatly anywhere else. It was also bigger and heavier than it looks, and had to be literally dragged around.
That ikea chair is also cräp. That thing buckled under 200 lbs of weight and never hung straight, the cushion would stick out of the side and have to be constantly pulled back, it was so reclined (and non-adjustable) that it would hardly make a decent gaming chair.
Just buy an adjustable height and back office chair - they roll and fit under tables for easy access and storage, adjust for comfort, and you can get a quite decent one for $100. For a chair you don't plan on leaving in one spot, wheels are never overrated.
Remember, a chair is a chair. These dont plug into your system or give you any extra lives, and they dont look nearly as cool in your living room as you'd think.