The default type for logic output drivers is push-pull. This actively pushes the voltage up when the output is high, and pulls it down when the output is low. There is usually no need for further resistors tied to either supply.
The exception would be when the output driver cannot source enough current to drive its load but can sink more than enough, or vice versa with the resistor tied to the "weak" supply in order to assist the driver. But 74HC devices usually have a decent amount of current available for actively driving a load.
Only when the output driver is open drain are pull-up resistors required, whether discrete or integrated into an IC. Tri-state outputs are usually connected together and no fewer than (and usually only) one output active in order to prevent the input they are connected to from floating.