From what I saw, i5-4690K is actually incompatible with the motherboard, it might work with a BIOS update though (gotta check more about it), like SugarD said above.
In my opinion, he would be better off with i5-4670K, performance gain isn't that major.
That's false and I'll contradict that. The processor is compatible with the motherboard, the processor uses sockel 1150 and the motherboard supports it. But as SugarD says, he may need to update the BIOS to get it fully working, although I'd still recommend to buy a motherboard that's z97 instead of z87.
One inquiry, why are you guys buying an mITX motherboard when the computer case supports ATX, mATX and mITX? Generally, mITX, the size of the motherboard are built in smaller computer cases that doesn't take up that much space. In general, ATX is the most common, but mATX and mITX is getting more popular nowadays.
I'd replace the storage hard drive and go for an SSD instead, an SSD will give you more performance and the computer in general will be more faster due to the speed that an SSD offers you. That hard drive that you've selected is mainly for storage so I wouldn't recommend installing OS and games on that. It do work to run Windows and games, but still, an SSD would be better.
As for the graphic card, it's two generations old, I'd go up a level and go for the 700-series, maybe a GTX 750/ 750ti or 760 that would suffice, and be cheap as well. I'll not say the graphic card is that bad but buying newer graphic cards is always advisable. If your friend have a higher budget he could go up even a level and buy the brand new cards from the 900-series, but that'd be more expensive. I cannot say he's obliged to buy a NVIDIA card but I'd recommend that, not the biggest fan of AMD.