PCIe 3.0 @ x8 is not "better known" as PCIe 2.0 @ x16, they are two different things and just happen to have roughly similar usable bandwidth.
PCIe 3.0 lanes run at 8Gbps each (x8 = 64Gbps) while PCIe 2.0/2.1 lanes run at 5Gbps each (x16 = 80Gbps) and the card will run with as many lanes enabled as are available on the slot at whatever the highest speed both endpoints support.
Since the Pentium/i3 only support PCIe 2.1 and the motherboard likely supports x16, the board should be running PCIe 2.1 x16.
The only common case where a GPU may end up running whatever version of PCIe at x8 or x4 instead of x16 is for SLI/CFX where the 16-lanes GPU bus may get split between two x8 slots or a mix of x4 and x8. Some (very) high-end motherboards (~$600) have PCIe switches that allow running as many as four cards at PCIe 3.0 x16.