Why is there a difference between the cosmic event horizon and the age of the universe?

From the link you provide:

The particle horizon differs from the cosmic event horizon, in that the particle horizon represents the largest comoving distance from which light could have reached the observer by a specific time, while the event horizon is the largest comoving distance from which light emitted now can ever reach the observer in the future. The current distance to our cosmic event horizon is about 5 Gpc, well within our observable range given by the particle horizon.

Your confusion somes from the fact that you are mixing to different horizons:

The particle horizon is the sphere centered on us that has a radius equal to the distance that light can travel in 13.8 Gyr (the age of the Universe). That is, light that was emitted when the Universe was born at a point on that horizon, reaches us today. Note that, because the Universe is expanding, the distance is not 13.8 Gly, or 4.2 Gpc, as one might naively expect, but in fact 47 Gly.

The cosmic event horizon is also a sphere centered on us, which holds all points from which light, if it is emitted today, it will reach us in the future. If it is emitted outside this horizon, the expansion of the Universe ensures that the light will never reach us.

As time goes, we will see light that came from farther and farther away, and thus the distance to the particle horizon is increasing. Meanwhile, the accelerating expansion of the Universe ensures that light emitted from distant galaxies in the future are able to reach us only if they are increasingly closer. Thus the distance to the event horizon is decreasing.

You can see the particle and the event horizons as blue and red lines in the plot in @Pulsar's great answer here.

The 16 Gly that the distance to the event horizon is today is sort of a coincidence. It has nothing to do with the age of the Universe. It only depends on the future expansion of the Universe, which in turn depends on the densities of the components of the Universe ($Omega_mathrm{b},Omega_mathrm{DM},Omega_Lambda$, etc.). If the Universe has been dominated by matter (or radiation), then there would be no event horizon: No galaxy, ever-so far away would not be visible to us, if we just had the patience to wait. A galaxy is 10,000 billion lightyears away? Just wait long enough (exactly how long depends on the actual density).

However, our Universe happens to be dominated by dark energy, which accelerates the expansion without boundaries. This unfortunately means that the light leaving today from a galaxy 17 Gly away will be carried away by the expansion faster than it can travel toward us. In contrast, the light emitted today from a galaxy 15 Gly away will travel in our direction, but will nonetheless initially move away from us due to the expansion. However, its journey toward us makes this expansion rate smaller and smaller (since the expansion rate increases with distance from us), and after a period of time it will have traveled so far that it has overcome expansion and starts decreasing its distance from us and eventually reach us after 100 Gyr or so.