Its a mini-tower. A Lenovo Thinkcentre M83.
oops, yeah, The HD 8xxx is actually not better than the 7970.
double checking AMDs own site, the 8xxx series is an OEM/mini series made after they flipped from the HD 7970 over to the R7/9 series name wise.
basically, yes 'normally' I would have been right wrt higher number is better, except in this one specific series... so my bad.
for direct compare of numbers:
7970 uses PCIe 3.0 x16
8570 uses PCIe 3.0 x8 (1/2 the throughput)
7970 tops out between 3.8 TFlops - 4.3 TFlops performance wise
8570 tops out around 560 GFlops (1/8th ish of the 7970)
7970 has 32ish compute units
8570 has 6 compute units
7970 is dx 11.2 (and can do dx12 stuff)
8570 is dx 11.1 (and may not do dx12 stuff, not sure)
the good news is that the HD 8570 is /slightly/ better than the min spec 5570.
it'd be worth the 200$ or so to upgrade. But since you're in a mini-tower/Lenova, that may be hard to do.
edit:
Modern top-of the line integrated graphics should be at or even above the HD5570, especially in a modern game.
It's a little bit strange that they have the 450 as "minimum" on the nvidia side though, back in the day the GTS450 was almost twice as fast as the HD5570
You'd think, but unfortunately not everyone gets the 'top of the line integrated' graphics cards when they pick up the random cheap prebuilt box (and/or laptop... which I have little clue as to if any laptop gpu could hit the minimum let alone come close to the recommended without being a seriously expensive laptop). Though, anything made in the last year or two should 'hopefully' be better than the 5570 -- which is an ATI card (tells you how old that is).