If you're building on a limited budget, I wouldn't bother with that relatively expensive CPU cooler, and instead put that money toward other components that will make more of a difference in performance, such as a dedicated graphics card. Here's one example of what could be done, but you might go with other components if the prices or availability differ where you are...
PCPartPicker part list /
Price breakdown by merchant
CPU: AMD - Ryzen 5 2600 3.4GHz 6-Core Processor ($165.99 @ Amazon)
Motherboard: Gigabyte - B450M DS3H Micro ATX AM4 Motherboard ($69.99 @ SuperBiiz)
Memory: G.Skill - Ripjaws V Series 8GB (2 x 4GB) DDR4-3200 Memory ($89.99 @ Newegg)
Storage: Seagate - BarraCuda 1TB 3.5" 7200RPM Internal Hard Drive ($42.89 @ OutletPC)
Video Card: MSI - GeForce GTX 1050 2GB AERO ITX Video Card ($119.99 @ B&H)
Case: Thermaltake - Versa H18 Tempered Glass MicroATX Mini Tower Case ($41.99 @ Newegg)
Power Supply: SeaSonic - 520W 80+ Bronze Certified Fully-Modular ATX Power Supply ($34.99 @ Newegg)
Total: $565.83
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-09-03 00:26 EDT-0400
In this example, I cut out the tower cooler and added a GTX 1050, which can get about double the gaming performance of a 1030 or the integrated Vega graphics in the Ryzen 2400G.
I also swapped the CPU for a 6-core/12-thread Ryzen 2600, which should only cost a little more than a 4-core/8-thread 2400G, and may get better performance in future games due to the higher core count. The 2600 doesn't include integrated graphics, but if you're using a dedicated graphics card, those won't be necessary. As another option if you're looking to cut costs to get the dedicated card, you could cut the processor down to something like a 4-core/4-thread Ryzen 2200G.
I also went with a B450 motherboard, since the 400-series motherboards are guaranteed to run AMD's 2000-series CPUs, while with a 300-series motherboard, you may potentially need to update the BIOS, which requires a first-generation Ryzen CPU to perform. I also picked a board with 4 memory slots, so that more RAM can be added in the future.
And for RAM, I cut it back down to 2 x 4GB sticks, since nearly all games still run well enough on that, and RAM is priced rather high right now. In the future, an upgrade to 16GB will likely be necessary to run the latest games though. You could of course go with 16GB now if you have the budget for it. Again, putting that money toward a graphics card would undoubtedly result in better gaming performance in the short term though.
The case is just a random inexpensive option, since I didn't see the one you listed at that site. And I went with a relatively cheap but decent PSU, though there may be better options depending on what prices are like in your area. If you are in a different country where the prices are significantly different, there might potentially be better options for any of these components.
Edit: I just noticed you had an SSD in your build, but I didn't include one here. It's certainly an option to include one as a boot drive, and maybe install a couple of your most played games to if you have the room. As far as gaming performance goes, an SSD generally won't help frame rates, but can improve load times. It's arguably a good thing to have in a gaming system, but again, not nearly as important for performance as a dedicated graphics card.