No, definitely not.
The Alienware X51 is not even a gaming computer. It is a desktop being marketed as a gaming computer. It has an integrated graphics chip by default, which is not powerful enough to be classed as a real gaming chip.
Also, you are asking about the processor, but the processor is much less important than the graphics chip or card.
You might as well forget about Intel iwhatever, because that doesn't matter.
What matters is that you have a GTX 750 ti or better graphics card, and the X51 does not, not by a long shot.
To make it a real (and minimally decent) gaming computer, you have to pay Dell $350 to put in a $240 graphics card.
The important thing you have to realize is that gaming computers, real gaming computers, are not cheap.
They cost a lot of money, usually 3-4x more than a gaming console. The reason for this is that they are usually 2-3x more powerful than a gaming console, even when new gaming consoles are released.
And to play games at the resolutions and framerates demanded by monitors, and at the quality gaming computers offer, you need that power to be competitive. It isn't like COD on a console where there is input lag and imprecise aiming. You have to have a smooth, high framerate rig because every twitch input you make really matters.
Here's a rough analog of my rig:
PCPartPicker part list: http://pcpartpicker.com/p/3r1ZO
Price breakdown by merchant: http://pcpartpicker.com/p/3r1ZO/by_merchant/
Benchmarks: http://pcpartpicker.com/p/3r1ZO/benchmarks/
CPU: AMD FX-8350 4.0GHz 8-Core Processor ($179.00 @ Amazon)
Motherboard: Gigabyte GA-970A-UD3P ATX AM3+ Motherboard ($79.99 @ Newegg)
Memory: Crucial Ballistix 8GB (2 x 4GB) DDR3-1866 Memory ($79.99 @ Amazon)
Storage: Western Digital Caviar Black 2TB 3.5" 7200RPM Internal Hard Drive ($134.99 @ NCIX US)
Video Card: MSI GeForce GTX 770 2GB Video Card ($319.99 @ NCIX US)
Case: Antec Nine Hundred ATX Mid Tower Case ($95.87 @ Amazon)
Power Supply: Antec EarthWatts Platinum 650W 80+ Platinum Certified ATX Power Supply ($69.99 @ NCIX US)
Optical Drive: Asus DRW-24B1ST/BLK/B/AS DVD/CD Writer ($26.97 @ Newegg)
Operating System: Microsoft Windows 8.1 - 64-bit (OEM) (64-bit) ($99.98 @ OutletPC)
Total: $1077.77
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-04-13 12:49 EDT-0400)
Except I have about $300 more in hard-drives and solid state drives, and am running W7.
A "budget" gaming computer would look like this:
PCPartPicker part list: http://pcpartpicker.com/p/3RDji
Price breakdown by merchant: http://pcpartpicker.com/p/3RDji/by_merchant/
Benchmarks: http://pcpartpicker.com/p/3RDji/benchmarks/
CPU: AMD FX-6300 3.5GHz 6-Core Processor ($109.99 @ NCIX US)
Motherboard: MSI 970A-G46 ATX AM3+ Motherboard ($69.99 @ Micro Center)
Memory: Crucial Ballistix 8GB (2 x 4GB) DDR3-1866 Memory ($84.80 @ Amazon)
Storage: Western Digital Caviar Black 1TB 3.5" 7200RPM Internal Hard Drive ($88.97 @ OutletPC)
Video Card: MSI GeForce GTX 750 Ti 2GB Video Card ($129.99 @ Newegg)
Case: Antec Nine Hundred ATX Mid Tower Case ($69.99 @ Newegg)
Power Supply: EVGA SuperNOVA 650W 80+ Gold Certified Fully-Modular ATX Power Supply ($74.99 @ NCIX US)
Optical Drive: Asus DRW-24B1ST/BLK/B/AS DVD/CD Writer ($16.99 @ Newegg)
Operating System: Microsoft Windows 8.1 Pro - 64-bit (OEM) (64-bit) ($129.98 @ OutletPC)
Total: $775.69
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-05-26 22:32 EDT-0400)
And then you still need to buy a monitor, keyboard/mouse/headphones, etc.