What would the centripetal g force on the payload be compared with simply shooting it out of a very large gun pointed skyward?
In comparing one force verses another acting on the same mass, since
f=ma are true for both cases (Newton's second law of motion), mass cancels out leaving you just comparing acceleration.
For the object orbiting around a center, V is the linear velocity while orbiting, and it equals the velocity at release:
Centripetal /centrifugal acceleration is
a = V2/R, here R is the distance to the center of rotation.
For the object being shot out of a barrel (or rail of a rail-gun), V is the exit velocity of the object when leaving the barrel
Shooting out of a gun is difficult to say since acceleration by gas-explosion is not constant while in the barrel. Let's assume it is constant acceleration like you can do with a linear motor catapult or rail-gun. With such assumption, while in the barrel, then:
Linear constant acceleration would be
a = V2/2L, here L is the length of the gun barrel.
So, if your gun is
half the radius of the centrifuge, your acceleration is the same and thus the force are the same. Of course, radius is just 1/2 the width (diameter) of the centrifuge.
I don't know about these SpinLaunch folks... I think building a rail-gun 25 meters in length would be easier than building a centrifuge 100 meters in diameter, and a linear rail is far easier to aim.