Telsa has been relentless in simplifying the part count of a tesla. Each part needs to designed, tracked, inventoried, installed, verified, made available for repairs, increases the size of the factory, and decreases the rate of production. Added parts also require space to install, clearance, sometimes custom tools, testing, might create vibration/wear/noise that requires mitigation, etc.
The front and rear chassis used to require 100s of robots and parts, and then alignment would have to be checked, more material used, more time, more robots, etc. Replacing the front and rear chassis removed 300 robots ... each, and of course the factory space for the robots, and the time for the assembly line to run past those robots.
The glass roof, which IMO isn't a big feature, can be installed after the chassis is built. Enabling robots to install the dashboard, central console, seats, etc before the roof is installed.
On most cars the dashboard is complex, multilayered, complex set of sensors, displays, spinning needles (speed, rpm, temp, fuel levels, etc). On a Tesla the dash is built on a big square straight piece of aluminum, a simple slot for airflow (no fancy/fiddly air flow controls), and a 15" display. Likely reducing 100s of parts.
The octovalve and related cooling system is a marvel as well, nicely integrating heating/cooling of the cabin, motors, and battery. Dramatically simpler than competing solutions, in particular the Ford Mach E and Lightning.
Most cars have an extremely complex set of CPUs, sensors, and control distributed all around the car. Chips in doors for locks/windows, a separate system for ABS (usually from bosche), networks of temperature/pressure/movement sensors, torque controls/monitoring for window motors, windshield wipers, airflow motors, etc. In the model 3 it's largely integrated into a single board at a level of integration Munroe claims they have seen in no other car, or even any product ... outside of a satellite.
This might sound like hand waving and marketing, but one metric that supports this is the cars products per square foot of factory per hour. Tesla is way ahead. It's also supported by high profit margins, even when compared to companies that have as high or higher prices.
So yes I'd say that the gigapress is a key part of reducing the part count, assembly time, and number of robots required to build a car. The result is a Tesla factory builds more cars than the competitions factory of the same size.