Actually the world isn't changing that much, the FAA and Nautical regulations still have language that require charts to be used (multi engine and commercial use aircraft and professionally operated vessels over 39.4 feet or over 1600 tonnes). As a pilot, I like the convenience of the GPS, but having experienced electrical problems in flight, GPS outages that can occur, and device failures, I always have a chart in my lap and routinely check my position on the chart during flight. Most all the pilots I know who fly their own aircraft have similar discipline. If the yacht captain is a professional with various ratings, he was probably right in saying he used his GPS phone gizmo most of the time to check on course, etc. But you can be sure the bridge watch had charts out not just for display of impressionable passengers, but as a navigational tool coupled with the electronics. As with aviation, most long distance travel requires the use of larger charts for a reasonably accurate view of the course and any changes that have been made. Anything not necessary for the safe conduct of the voyage/flight is usually not just laying around given cockpit and bridge resource/space management needs. If they are laying about and not being used for reference its not a very professional demonstration of good seamanship.
As pointed out, GPS is a tool that really depends on where you are and what you are doing that dictates if having either a map, a GPS, or both is a good idea. FWIW, I tend to carry maps all the time, with GPS as a back up tool on unfamiliar terrain. As Elf points out, the AT is a unique, well marked and worn trail that GPS is fairly well suited for and is often said to be all one needs. However, that advice may not serve well on other trails that are less worn, marked, and maintained. An electronic failure of any cause could prove to be a real problem.