Got your PM, $500 isn't much of a budget for a laptop but I've had to work with less in times of desperation. Luckily that game doesn't have high system requirements and you may be able to get by on a laptop with integrated GPU thats brand new, or you may want to look for refurbished laptops on NewEgg or eBay.
I can find some decent brand new ones under $700 brand new but they are in the mid to high $600's price range. Lenovo also has some good laptops for a good price if you don't want to go with an integrated GPU, here's two I found on NewEgg you may be interested in: