You don't list a video card so it is a little difficult to assess performance. Settings have an impact on FPS, especially if you are at the higher resolutions. If you are using the integrated graphics on the A6 then this is the performance
http://www.game-debate.com/games/index.php?g_id=1249&game=DOTA+2&p_make=AMD&p_deriv=APU+A6-7400K+Dual-Core&gc_make=ATI&gc_deriv=Radeon+R5+7400K&ram=8&checkSubmit=#systemRequirements
Not sure if you have purchased your parts yet but I will propose a different build. If you are intending to use the integrated graphics then it is even more important that you don't buy the A6-7400.
First, I put your suggested part into PCPartPicker to get a price. I then took that budget and came up with a Kaby Lake build for approx. the same. Both these builds are below.
The integrated graphics will be better
http://gpu.userbenchmark.com/Compare/AMD-Radeon-R5-vs-Intel--HD-610-Desktop-Kaby-Lake/m12264vsm225196
And the G4560 will crush the A6-7400K
http://imgur.com/a/EIFBR
https://www.cpubenchmark.net/
The one thing that you have to mindful of with this build is that the BIOS has to be at revision 7.10 or later for this CPU to work. Otherwise you will need a Sky Lake CPU installed to update the BIOS. But rev. 7.10 was released on 27-Oct-16 so a good chance that it will be okay. If you are buying at a store then might be able to look at the package to determine the BIOS revision.
PCPartPicker part list:
https://pcpartpicker.com/list/NWnWCy
Price breakdown by merchant: https://pcpartpicker.com/list/NWnWCy/by_merchant/
CPU: AMD A6-7400K 3.5GHz Dual-Core Processor ($46.74 @ Amazon)
Memory: Kingston HyperX Fury White 8GB (2 x 4GB) DDR3-1866 Memory ($59.99 @ Amazon)
Other: ASUS Micro ATX DDR3 2400 NA Motherboards A68HM-K ($49.99 @ Amazon)
Total: $156.72
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-04-19 09:13 EDT-0400
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PCPartPicker part list:
https://pcpartpicker.com/list/NsRzWX
Price breakdown by merchant: https://pcpartpicker.com/list/NsRzWX/by_merchant/
CPU: Intel Pentium G4560 3.5GHz Dual-Core Processor ($59.48 @ OutletPC)
Motherboard: ASRock H110M-DGS Micro ATX LGA1151 Motherboard ($52.99 @ SuperBiiz)
Memory: Patriot 8GB (2 x 4GB) DDR4-2133 Memory ($50.00 @ Amazon)
Total: $162.47
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-04-19 09:20 EDT-0400