The games that "require" a quad only look for 4 logical processors which means 4 threads. An i3 has HT which gives it 4 threads. I put up
video showing a Sandy Bridge (2nd gen) i3 (I disable 4 cores to showcase an "i3") paired with a 970 gaming just fine on the supposed required 4 core titles. A Skylake i3 is as fast and mostly faster than an overclocked 8350 at all games and even a lot of multithreaded tasks so there's no reason to go with an AMD processor until maybe Zen.
My article is a bit outdated and I need to sometime soon update it for DX12, but a lot of people have been asking. The deal with that is it's not guaranteed to utilize more cores, it only has the better capability of properly utilizing them. The proper advantage of DX12 and Vulkan (or other low level APIs like Mantle that's now defunct) is the reduction of CPU bottleneck due to requiring less CPU overhead. Basically, developers can now properly program to directly translate to "bare metal" or straight to GPU requiring less data flow and bottleneck by the CPU. These APIs have the ability to utilize more cores for an enhancement in AI, CPU physics, and other technologies BUT the issue with that is the average person has 4 or less threads. With Intel sticking to a 4 core design as their mainstream we will not see thread utilization increase until they change this. With the FX line being 4 years old now we are seeing a huge influx in transition to Intel as people "see the light" so to speak and with that popularity being on the rise we won't see any increase in thread usage until the industry moves on from this "standard". Not to mention, the mass majority of people are either not DX12 capable or have the bare feature requirement meaning most games coming out in the next 2-3 years will still be heavily DX12_0 feature capable and will only utilize that low CPU overhead byproduct of DX12. Maybe with Canonlake we might see an increase to 6 core mainstream for the i7, but don't hold your breath. So you're good with 4 threads now, and can upgrade yourself later an i5 or i7 if need be but probably won't be necessary unless you go with a much stronger GPU.