Can this PC Run games like csgo and league of legends well?

That's a decent budget/mid range build. And yes, that's good enough to play those games with ease. But I suggest few changes:

- The Gigabyte GA-B85M-D3H is a B85 chipset board which may require a BIOS update to even recognize the Intel G3258, which is a Haswell Refresh. So if you want everything to work out-of-the-box, get the Gigabyte GA-H97M-D3H, which will support that processor without the need for any BIOS updates. This H97 chipset board also allows you to upgrade in future to any Haswell Refresh processors i3 4150/4160, i5 4460/4590/4690, i74790 etc.

- Corsair CX500W is a "Tier 3" PSU with comes with cheap capacitors. So its longevity is questionable. There are mixed experiences among consumers with this PSU. I suggest you to consider at least a quality "Tier 2" PSU. The Antec HCG 520W is a quality "Tier 2" PSU that can deliver a solid 40Amps on its +12V rail, which is more than enough to power up your entire rig. It also gives you the option to upgrade in future to NVIDIA GTX 960/970/980, AMD R9 270X/280/280X/380/R7 370 etc.

- Also there are pretty good budget cases that will get the job done available than Cooler Master Enforcer. As in a budget build spending AUD $108 on a case is not good.

- MSI GTX 750 Ti Gaming is a better option, as it comes with Twin Frozr Cooling Tech, one of the best in the industry, that offers near silent operation, stability and performance.

Why Gigabyte Motherboard and MSI Graphics cards?

Because they make stable, durable and performance oriented product with lowest RMAs. See the images below:

What is RMA?

Return Merchandise Authorization (RMA) is a part of the process of returning a product in order to receive a refund, replacement, or repair during the product's warranty period.

Gigabyte with least RMA percentage over the past two years

Major Motherboard and Graphics Card Manufacturers RMA Ratings

Read the full article here - Reliability report: Gigabyte top for motherboards, MSI for graphics cards
Just hold let me look into it and give you an alternative, better price to performance value oriented build.

Update:

Even when you're on a budget try to come up with a build that gives you better future upgrade path without compromising your current needs.

Keeping that in mind I've updated the build:

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Pentium G3258 3.2GHz Dual-Core Processor ($89.00 @ Centre Com)
Motherboard: Gigabyte GA-H97M-D3H Micro ATX LGA1150 Motherboard ($125.00 @ Centre Com)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory ($82.00 @ Umart)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($70.00 @ IJK)
Video Card: MSI GeForce GTX 750 Ti 2GB TWIN FROZR Video Card ($191.00 @ IJK)
Case: Corsair SPEC-03 Red ATX Mid Tower Case ($85.00 @ CPL Online)
Power Supply: Antec High Current Gamer 520W 80+ Bronze Certified ATX Power Supply ($95.00 @ CPL Online)
Optical Drive: LG GH24NSB0 DVD/CD Writer ($19.00 @ IJK)
Total: $756.00
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-07-04 21:28 AEST+1000

This is a solid build that meets or even surpasses all you expectations. Offers great price to performance value and at the same time, gives you the option to upgrade further in future.

Cheers!