On the Zero there are only ports A and B, but they're 32-bits wide and not all the pins on each port are available. The Zero's SAMD21G does have direct access both the data direction and the output registers, as well as the option of the set and clear registers like the Due.
The registers you're probably interested in are:
REG_PORT_DIR0: Data direction register for port A
REG_PORT_DIR1: Data direction register for port B
REG_PORT_OUT0: Data output register for port A
REG_PORT_OUT1: Data output register for port B
You can set a bit in the register by calling on the port pin definition, for example:
REG_PORT_DIR0 |= PORT_PA17; // Set digital pin 13 to an output
The problem with setting the whole port on the Zero is that there's a limited number of pins and some are used for other peripherals like its native USB, I2C and EDBG communication. Setting the port on these pins will have no effect, unless you reconnect the port to pin using the port multiplexer.
By the way, it's also possible access the port in the same way on the Due by writing to the PIO_ODSR (Output Data Status Register), but the corresponding bits in the PIO_OWSR (Output Write Status Register) must be set first.
Here's a quote from the SAM3X datasheet:
Figure 32-4 shows how the outputs are driven either by writing PIO_SODR or PIO_CODR, or by
directly writing PIO_ODSR. This last case is valid only if the corresponding bit in PIO_OWSR is
set.