It depends which Alienware Alpha you are aiming for, the lower end model does not meet the minimum requirements, the higher end ones should run the game fine.
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This error is caused by Windows UAC blocking the installer/game, the game itself is fine and I have not been able to reproduce this error on any computer I have access to.
I suggest anyone having this error to adjust their settings temporarily to install the game. Googling the error code will get you a guide on how to do that.
This error is usually a problem with Windows rather than an individual application. Often caused by Windows UAC blocking unrecognized programs from being installed/run correctly.
Try running the game as an administrator.