$250 is too low. But the whole setup with MBA with 512 GB SSD, 8 GB RAM and i7 CPU, the GPU and then the $250 in parts is not only enough money for powerful desktop computer, it is enough money for cheaper MBA variant and then powerful desktop computer.
The OP costs $250 + GPU + Windows license, and doesn't have a case. It's also quite likely that the OP is also using an external hard disk rather than putting Windows & a few large games on his SSD. If so, $250 can get you a MB/CPU/RAM/PS.
Pretty sure they're referring to the cost of the computer + parts...Also, its like $400-500 for parts unless you have a [fairly] recent graphics card just sitting around