Not that I'll ever get my mother on a plane to go to WDW again, but I was looking for this very information a year ago or so when she was fitted with a hearing aid with the T-coil system. The WDW page is confusing as heck and outside information is scarce but I finally got enough information to ask some better questions and this is what I found out.
So you've read the "Services for Guests with Hearing Disabilities" page and there is a section there on "Assistive Listening" devices. That paragraph alludes to "amplifies sound through headphones or an induction loop at specific theme park attractions." and you think, "oh cool, those locations must be set up for telecoil broadcast."
Nope.
They are set up for a system that's ... actually kinda cool. A company called SoftEQ, that bulds captioning software took Disney's SynkLink attraction synchronization protocol and developed the Durateq device with collaboration with HP using HP's iPaq handheld PDA platform. All very high tech back in ... like 2002 but the system has actually aged very well and most find it is a pretty cool bit of tech.
I'm making an informed guess here, as I've never had one in my hands, but the Durateq receives the assistive audio (or visual subtitling ... it has a screen) synchronized to the attraction. It has a headphone jack, and the induction loop mentioned at the beginning of that paragraph refers to a t-coil listening loop that you can plug into the device instead of regular headphones. the listening loop wraps around your neck and converts the headphone speaker signal into the electromagnetic waves your hearing aid t-coil can pick up.
It sorta says this at the end of that paragraph but they didn't really do a good job of it... "It is recommended that you bring your own headphones or induction loop as the device has a standard headphone jack."
I hope that helps ... a list (that may be current) of attractions that support this device can be found
here.