The most important piece of hardware for games, is the graphics card. As these days, just about any laptop that comes with a reasonable to good (or better) dedicated graphics card will easily meet & exceed most games' other system requirements like CPU, RAM, HDD, etc so you don't have to worry about the other components.
Bigfish games seem to be Flash-based only (?), & if so, shouldn't be a problem at all. I had a look into the system requirements for CSI games, which I'm assuming are these click here, with system requrements for CSI Fatal Conspiracy at click here, & they don't appear to be taxing either. But I don't think onboard graphics (the type most laptops come with) will be good enough, so I'd recommend getting a laptop with a dedicated graphics card.
Does she have a preference for any particular screen size? G