Can a petWALK pet door also recognize older FDX-A chips?

No, these chips have a 10-digit identification number. Today 15-digit FDX-B chip numbers are common with a country code in Europe. The FDX-A pet chips, however, are not common in Europe. It could happen that an imported (from overseas) pet is equipped with such a chip. In this case you can use a RFID fob, or your vet additionally injects a corresponding chip.