Yes, games could be played with a shared graphic card. But as they are less powerful they will not perform better then a non shared graphic card
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Counter strike has pretty amazing graphics, so you cannot play CSS w/out a graphics card. You can play CS 1.6 without a graphics card but CS:S is impossible to play unless you have a graphics card.
That card is not powerful enough to play Carbon. You'll need a more robust system.
yesss
yes
Yes, because the recommended graphics card is, well, just that: a recommendation. There should also be something that says minimum system requirements, which is what you need to have at the minimum to run the game.