http://www.msy.com.au/vic/clayton/notebooks/13429--gigabyte-p15fv2-850-4702s-i7-4710mq-8gb-1tb5400-156fhd-dvdrw-win81-64bit-2gb-gtx850.html may be slightly over but this will be the best for your money imo
Integrated graphics capabilities of the newer gen i5/i7 cpu's will handle those gaming titles.
Id personally go with >> http://www.shoppingexpress.com.au/buy/lenovo-thinkpad-l430-laptops-24682e8-14-inch-intel-i5-3320m-4gb-500gb-dvdrw-win7-pro-64/24682E8
a proper resolution screen, nice keyboard all I'd do is add a msata ssd to decrease boot times etc using either Lenovo's cache software or migrate the os to it entirely.
Any dedicated mobile gpu less than a 860m is a waste of battery and money imho.
If you're comfortable enough with buying second hand try your hand at ebay or gumtree. Here in Perth theres a fair few gaming laptops for sale from FIFO workers. I've seen good ones with 7970m's etc for <$500.
To buy a new proper gaming laptop here in oz with our shit prices its going to be hard.
If modern ThinkPads are anything like the older one's, they are built like absolute tanks. I know people at school who have 5, 6, 7+ year old ThinkPads that still operate flawlessly. Of course, they won't play games, but they are great for programming.
Ever considered a System76 laptop? This machine is reasonably priced and come's preinstalled with Linux (you can always install Windows if you like). My laptop has Intel Iris (Intel HD 5100) and I play games that are more intensive than the ones you listed. This laptop has Intel Iris Pro (Intel HD 5200) and an Intel i7-470hq so you should be good. https://system76.com/laptops/galago