[slededit]

For obscure things like this its cheaper to chain more common components together through an intermediate protocol. So your PCIe adapter may well be an on-board PCIe USB host -> parallel port controller, done with off the shelf ICs. This prevents the need for a custom ASIC which is unlikely to be economical here.

[probablybanned]

This is sometimes the case, but the most popular cards on the market are indeed single chip ASIC solutions.

Also, don't forget that small FPGAs like those from Lattice Semi are very cheap these days and find a lot of use specifically in obscure IO interfacing tasks.