Yes well technically you need only spend $100 to make a gaming computer so long as your definition of games are anything DOS-Era, and Mine Sweeper....
Simple, it doesn't need to run BF3 or Crysis maxed. Just it runs it on moderate graphics it's enough to be called a gaming computer. My laptop from school that uses shitty integrated graphics as opposed to a dedicated GPU can run some less demanding games like minecraft, portal and even call of duty.
It uses an i3 CPU and has 4 GB of RAM.
The term "gaming computer" has gotten pretty vague and many people associate it with a high-end computer. My definition is rather a computer that's decent enough to play some games on. Look at the price of consoles for example.
A high-end computer to me would be something more like mine with an i7 CPU and 16GB of RAM which is made for media and rendering. And before you say it's overkill, I've actually made good use of it. Had 90% RAM usage few times!