Welcome to bleepingcomputer!
That computer won't play any of those games at all. It's not really a bad deal because of the 22" monitor, but it has Intel integrated graphics, which won't play modern games well or at all, and the processor is pretty slow. For a processor, don't go less than an Intel core 2 duo, or an AMD Athlon 64 X2.
To play those games, you're probably looking at a computer around $700-$800 if you build it yourself, not including a monitor, mouse, keyboard, etc.
Now, you could buy that computer and throw a graphics card in for about $100-$150, but you may need a new power supply, and the processor is still going to slow you down a bit.
"I think there is a world market for maybe five computers." - Thomas Watson, Chairman of IBM, 1943