He's buying a Lenovo Y560 which is a laptop. Keep that in mind when you suggest video cards alyoshka.
Laptops generally SUCK for video games. Battlefield 2 does indeed like Quad Core CPUs. But it can be played on a dual-core. Being that you're looking at a laptop, you'll be playing at lower resolutions. This is good for you, especially with a lower end graphics card like the mobile 5730. The resolution on the Lenovo Y560 appears to be set at 1366 x 768 and is not upgradable. So you should be able to get away with playing games on it at such a low screen resolution. Just keep your graphic settings down.
Lenovo offers the i5-460M which is a Dual-Core (with Hyperthreading) processor. This is definitely faster than the i3 option, but don't like Hyperthreading fool you. It's basically useless for games. So it's still a dual-core processor, just a beefier one. I'd still recommend going the i5 route if it's affordable ($50 upgrade the site shows). You get a little faster CPU, plus the i5 line supports Turbo Boost, which means the CPU sort of overclocks itself when you really need it. Though the effectiveness of such a feature while pushing both cores is probably questionable.
Here's what you can expect with the ATI 5730 GPU:
http://www.notebookcheck.net/ATI-Mobility-Radeon-HD-5730.23825.0.html
Battlefield: Bad Company 2 played @ 34FPS as an average (they don't denote actual resolution). I'd probably want to play @ Medium to keep FPS above 30, especially if you're doing multiplayer stuff.