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...But I'm not very tech savvy. To be honest,I don't care too much about it's specs but the nightmare scenario would be being unable to run Doom as I know it now. My understanding is that most posts fix all but I'm not certain so... Is there anything I should avoid or keep in mind before I buy?
Intel graphics are more than adequate for a game as old as Doom 3. Don't get caught up in the idea that laptops are good for gaming. Graphics advances may have stifled in the past years, making them run well on almost anything, but that's no reason to go out and spend $1000 on a laptop with a big honking GPU in it.
The matter isn't that it might "cut" it on paper if you simply count the number of unified shaders or pixel pipelines or clock frequency. If that was the ONLY factor, they yeah, Intel might be indeed suitable for an 8 or 10 year old game.
The real reason why Intel crap is unsuitable for games is that they never have dedicated memory, and furthermore, unlike e.g. ATI or NVidia in a similar situation, the shared memory size cannot be controlled and fluctuates dynamically (aka uncontrollably).
The result? Some games might work fine, while others will refuse to start at all, confused by the shitty drivers reporting conflicting information. Fact.