In my experience, most current types of artificial field surface do a really great job of quickly clearing moisture... until they don't.
The performance of the turf in wet situations is directly dependent on the way the site was prepped. I don't remember seeing enough site prep photos to verify if the install was done this way, but usually you'd prefer to see a concrete curb and gutter system installed first, followed by backfills of gravel then sand, before the turf is laid.
Under average conditions, this setup would last about 10 years, before the mat would need replaced and the undersurface to be compacted and reset. I'm not sure how the nightly traffic at a place like WDW, which will be much more sedentary than the active movement these surfaces are usually designed for, will affect the lifespan of the product.