The MB type is not the most important component for the game PC. The i3 is good for the game.
When you build the pc for game, you need do the homework, like for the MB/CPU compatibility, in the manufacturer to check the cpu support list. ASUS H81M-K cpu support list http://www.asus.com/uk/Motherboards/H81MK/HelpDesk_CPU/ and you can see the i3 4130 is in the list, and it need the MB has the 0304 version BIOS to support it. And in the download section you can see the BIOS 0304 is the 1st version, so they are compatible.
And next find one GPU you can afford to buy. Here is the Best Graphics Cards For The Money
http://www.tomshardware.com/reviews/gaming-graphics-card-review,3107-7.html and also make sure you have the PSU to power up the GPU. PSU requirements for the GPU
http://www.realhardtechx.com/index_archivos/Page362.htm And don't buy the nobrand PSU, not all the PSU are same. You need to buy the tier 3 one at least , but higher is better. PSU tier list
http://www.tomshardware.com/forum/id-1804779/power-supply-unit-tier-list.html
Then you need to find the review for the games you want to play to see how the GPU doing for it.
Like BF4
http://www.techspot.com/review/734-battlefield-4-benchmarks/page2.html
Shadow Of Mordor
http://www.tomshardware.com/reviews/shadow-of-mordor-performance,3996.html
If you want you can list the budget and where you want to shop, and we can find them for you.