What about buying a refurb laptop with a warranty and an NVidia GTX card in it that would stretch the performance you can get for that $600? It would be able to handle those games as well as potentially newer titles if something comes out that you have interest in.
Some people say absolutely NO to buying a used computer, but I have saved lots of money by buying second hand higher end computer components and whole used computers from trusted sources and you can get a bargain on better performance hardware by not paying the premium of new. Only drawback to used laptops is that the keyboards on them usually show some wear pattern in them from heavy keystrokes, so I usually go for desktop computers that are used vs a laptop that is usually sold with worn keyboard from prior user(s) heavy typing.
If interested in some gaming laptops that are refurbs for $600 I can look online and try to find you some.
Here is an example of what $600 can get you if you buy a refurb laptop. But this is sold out currently:
https://www.newegg.com/shale-black-acer-nitro-5-an515-51-5082-gaming-entertainment/p/1TS-000X-00S56?Item=9SIACA16JV4581and one with newer 8th gen CPU with a HDD vs SSD:
https://www.newegg.com/p/N82E16834316560?Item=9SIACA18P57250Lastly the $600 budget is pretty tight for a Gaming Laptop budget but it can be done. You can cut cost of a laptop even further if you take the risk of buying through ebay. But I dont buy computers through ebay, I only buy used components there like RAM or a CPU etc to cut corners in cost of a build but by which the health of the part can be determined quickly and if I get burned I am only out like $10 or $20 etc which makes it worth the gamble to save like $40 from elsewhere. I do look at the feedback ratings of sellers and if they have like 500+ positive feedbacks and seem legit i will spend more money at those sellers on ebay with lesser risk of getting burned.
Another place that i buy parts from is Amazon and they also sell refurb computers as well as used computers that aren't cleaned up as much as a refurb would be. I used Amazon for buying a used PlayStation 3 for example for $75 for my daughter when the PS3 she had cooked and died in summer heat while running. Everywhere else the used PS3's were like $130+. i took the gamble of buying a used PS3 through amazon and it paid off I just needed to go through an ownership process with Playstation Network and once I proved I was owner of the system it was then linked to my games and all set to go as I found out that PlayStations that are used are still registered to prior owner and until you get it registered with your account its a paperweight. But 25 minute tech support and all better with it registered as ours vs prior owner of GASMAN of all names