The card doesn't implement properly Legacy Interrupt support, or the support is bugged.
Similar problem happens with VIAUSB2/Firewire PCI cards for example. Them only can work with MSI/MSI-X style interrupts, and the legacy interrupt support is optional, it is poorly implemented, or it doesn't exist at all. This means these "PCI" cards will only work properly on Pentium 4 era chipsets and onwards, which have MSI/MSIX interrupt support properly implemented (firmware/chipset/APIC levels complete and full working).
You would like to test your card in P4+ era logic board if you have one. To discard it being a dud.
If it does indeed work, then you have one of these P4+ PCI cards.
EDIT: Datasheet says chip offers both Legacy and MSI interrupts (has a dedicated INTAB pin for legacy interrupt support). So at least signal support is there in the chip.