I personally think many folks do NOT really test the games thoroughly before they give an opinion
I have been using my Phenom II 955 at 3.5-4Ghz for the last couple of years with a Radeon 7870, the vast majority of games out there I can run very well at high settings 1080p no problems the few that I "have trouble with" I just adjust shadows or drop HBAO to SSAO and things like that.
Ryzen is WAY WAY faster then Phenom II is, a clock for clock difference, would likely have to run Phenom II x4 or x6, or Bulldozer/piledriver in the range of probably around 5.4Ghz to be "comparable"
So in my personal opinion, if I never had a problem running the vast majority of games, I doubt you would, games like GTA V are incredibly unoptimized and very much work better at high IPC designs like Intel or the speedy "simple" design Nvidia uses (basically like an Intel CPU but for graphics)
This is just my personal opinion based on thousands of hours testing the crud out of my specific system, I do not use the very fastest memory or the highest clock speeds I know my cpu and gpu are capable of
The cpu in this case that you reference will actually feed the 7870 far better than my Phenom II is capable of at 720p-1080p etc, but the flat response dontlistentome gave you as an "answer" I simply do not agree, some games absolutely, but am pretty sure some of those games are far more biased towards Intel and Nvidia to begin with.
the 2gb Vram "hurts" a bit there is no doubt about that, but there is a reason why most games have tons of things you can adjust, if anything Ryzen will force a bottleneck on the graphics card because it "overpowers it"....when I checked to see a potential bottleneck for my own purchase, RYzen 1400-1500 was quite well paired with it, and TBH if you drop the resolution down too much you can actually create a problem that may not actually exist because it is not loading the graphics card fully (shaders, TMU, ROP etc....just like any engine or power supply really, if you load it too lean it does not fully activate and if you load it too heavily it "chokes"
This site can "help"
http://thebottlenecker.com/...basically a Phenom II 955-980 (or better which is VERY easy to do) level is perfectly paired with a 7870-7950-7970 +/- a bottleneck, whereas with Ryzen 1400 using the same 7870 there is around a 20% bottleneck (the cpu is too powerful) whereas pairing with an RX 460 or better would match up VERY well, that is the graphics card is "fast enough" for the cpu to feed it well, overclocking can help of course, or for that matter, slowing the cpu down a bit.
in your case, the A10-7700k and 7870 will be matched PERFECTLY with only about a 3% bottleneck (which is basically nothing) if upgrade to Ryzen basically everything will bottleneck the graphics card (again overclocking or downclocking can mitigate this by all means) Ryzen over Phenom as per example there seems to be about a 1Ghz advantage in "speed" per core.
Anyways, running very low resolution absolutely will murder whatever performance you should be getting (and look like crap)..Ryzen do not do the greatest at running "high speed" that is their IPC is not made for very low resolution, they are built to compliment a decent graphics card 720p IMO is a joke, they are way too powerful to be held down this way, but, if one lower the clock speed on them (because money is tight) than by all means a 7870-270x with Ryzen 120 through 1800x will work very well....
anyways am done ^.^