It will not be a particularly good $600 laptop for games. The Radeon HD 8510G's performance is basically between the Intel HD 4400 and the Intel HD 4600 / Intel HD 5500 (5th generation Intel Core CPUs) integrated graphic cores.
For $599 + tax you can buy the 15.6" Lenovo Z50-70 with a dual core i7-4510u and a nVidia GT 820m. The CPU and the GPU are a lot more powerful than what the HP laptop has. The Z50-70 has a 1920 x 1080 screen but do not expect to play many games at that resolution with a mere GT 820m. That graphics chip is best suited for playing games at 1366 x 768 or 1600 x 900 resolution using low or medium graphics settings depending on how demanding the game is. If the game has really low graphic requirements (like League of...