The Asus card takes - UP TO - 16 pci-e lanes and makes 4 groups of 4 pci-e lanes, and connects each group to a m.2 connector.
This can work only if the motherboard and the bios support a feature called bifurcation. If this feature is not supported, then the 3 other m.2 connectors simply won't work.
Also, keep in mind that some pci-e slots only have 8 pci-e lanes, or even 4 pci-e lanes. If this is the case, only 2 m.2 connectors will work (8 pci-e lanes are split in 2 groups of 4 lanes) or a single m.2 connector.