As mondite said, it's a hybrid / mongrel / b'stard.
One axis of the Phillips cross has been extended out to the side so an ordinary straight screwdriver can be used. You see these on electrical connections or cheap bike parts as they try to cater for as many DIY bodgers as possible to use the one screwdriver they own.
When looking for a replacement, the important aspects are the thread type, length, diameter and head shape. Assuming you have the choice of screwdriver, then either a Phillips or a plain crosshead will do.