I would prefer to say that the Gaussian wave packet is an example of position-momentum uncertainty.
All wave packets, no matter what shape, have a position-momentum uncertainty relationship ΔxΔp = k, where k depends on the shape of the packet. The Gaussian wave packet is special because it can be shown from Fourier analysis theory that it has the smallest k, namely [itex]\hbar / 2[/itex]. All other shapes of packets have larger k's. Therefore for any wave packet,