The real turning point was probably around 2007 - 2009 when smartphones started getting decent GPS chips and data plans became more affordable. Before that, even people with GPS devices in their cars often still printed directions as backup - you'd have your Garmin or TomTom, but you'd grab those MapQuest pages just in case the device glitched or the roads weren't mapped right. There was definitely overlap where both systems coexisted in people's cars for a solid five years or more.
What's interesting is that the shift wasn't driven by a single technology so much as by the combination of better mapping data, faster mobile networks, and the normalization of having internet access while driving. Google Maps on the iPhone came out in 2008, and that made a huge difference because it was free and worked better than a lot of the paid GPS units people had bought. But even then, plenty of people kept printing because they didn't want to drain their phone battery or pay for data while navigating, especially on longer trips. Your dad's 2005 stash was actually peak printing era - right before the smartphone revolution made it obsolete, but well after GPSs were available. So yeah, finding those printouts is a pretty good snapshot of that transition period.