"x16 PCIe compatible" doesn't mean it's a x16 slot. It means if you put a x16 PCIe card in there it'll physically fit and work.
The way PCIe works is it's connectors are made up of a varying number of lanes, which is what the "x4" or "x16" refers to. You only need one lane for PCIe to work, and extra ones just make it faster.
So when you say "x4 PCIe link" and "x16 PCIe compatible connector", what that means is that the connector is the correct size for a 16x card to fit, but only wired up for x4. The extra pins don't connect to anything, but it's compatible in the sense something plugs in and works.
