A:AnswerThe HDMI cable should work just fine. If your alienware computer is old, you might need a DVI adapter. Those you can get anywhere. Hope this helps.
A:AnswerI don't belive this monitor would be good for gaming. The resolution is too low. You would want a 4K/UHD monitor to truely enjoying any kind of gaming.
A:AnswerAbsolutely! Desktop or laptop, this monitor is compatible! Determine what outputs your computer has (VGA, Display Port, HDMI). It comes with an HDMI cable but you should be able to use the same cable you use now unless DVI.