I don't think you are going to find a laptop with a backlit keyboard for under $300. Most laptops sold for less than $500 do not have a backlit keyboard.
CS (CS:GO?) and TF2 are not very demanding games so it is possible to run them on a $300 laptop. DayZ... probably not especially since I read that people with powerful desktops have problems in cities.
The only laptop with a backlit keybaord for under $500 that I am aware of is the following $330 Acer laptop.
https
/www.amazon.com/Acer-Aspire-i3-7100U-Windows-E5-575-33BM/dp/B01K1IO3QW/ref=sr_1_1?ie=UTF8&qid=1479479892&sr=8-1&keywords=i3-7100u