Hello, Lateralus!
It is possible to beat the Alpha in price - but not in convenience: the case I've listed here is a little bigger, hopefully small enough for your purposes.
PCPartPicker part list / Price breakdown by merchant
| Type | Item | Price |
|---|---|---|
| CPU | Intel Core i5-4460 3.2GHz Quad-Core Processor | $179.49 @ SuperBiiz |
| Motherboard | MSI H81I Mini ITX LGA1150 Motherboard | $63.99 @ SuperBiiz |
| Memory | Crucial Ballistix Sport 8GB (1 x 8GB) DDR3-1600 Memory | $54.99 @ Amazon |
| Storage | Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive | $47.97 @ SuperBiiz |
| Video Card | MSI Radeon HD 7950 3GB Video Card | $139.00 @GPUShack |
| Case | Antec ISK600 Mini ITX Tower Case | $39.99 @ NCIX US |
| Power Supply | Corsair Builder 430W 80+ Bronze Certified ATX Power Supply | $39.99 @ Amazon |
| Operating System | Microsoft Windows 8.1 (OEM) (64-bit) | $93.99 @ NCIX US |
| Prices include shipping, taxes, rebates, and discounts | ||
| Total | $659.41 | |
| Generated by PCPartPicker 2015-03-06 18:30 EST-0500 |
The OS was one of the biggest problems, since it eats up 15% of the budget. The GPU is refurbished, from GPUShack, nice for the price, and comes with a 2-year warranty. It is not close to the GTX 780 Ti, but the Alienware Alpha is much further away. Here's the gaming performance comparison, for the Alpha and This build.
Hope it helps! =)
Feel free to ask anything.