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 Legends), then playing at 1920 x 1080 should be possible.
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/shop.lenovo.com/us/en/laptops/lenovo/z-series/z50/
Beware, in the somewhat recent past Lenovo has installed a software called "Superfish" onto many of their consumer level laptops. It has been discovered to be malware and should be removed if present. Click link below for Lenovo's instructions on how to remove Superfish.
http/support.lenovo.com/en/product_security/superfish_uninstall
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