Both the EEPROM and the PCF8574A use the I2C communications. At the bottom-right of the schematic you will note two pull up resistors on the lines that connect the I2C bus to the 5 chips.

So, the micro controller will use I2C to address the desired device as needed. EEPROM for storage and retrival of the data. PCF8574A for the actually setting the values for each element of the matrix.

That's the simplified overview.

HTH,
SteveB