I know why he chose to do a Top 12. A cube has 12 edges. Simple geometry.
Anywho, I don't think I ever even owned 12 GameCube games. Nintendo was going through an odd experimental phase at the time, which was kind of off-putting at times (e.g., Sunshine was the only mainline Super Mario game I didn't care for), and seeing as how I was huge into collecting anime DVDs at the time, my remaining budget for entertainment made me a lot more selective about what I spent that remainder on. Most of what I played I borrowed or rented. There were several major titles I skipped entirely. Overall, there were only two standout titles for me on that system: Rogue Squadron II and The Wind Waker.
And to be honest, there weren't a ton of standout titles on the other systems, either. I felt the rest of the industry still hadn't fully gotten the hang of developing compelling 3D games, and with Nintendo making a lot of risky changes to many of their core franchises, that left precious little that generation that I truly enjoyed. My all-time Top 50 has generally consisted of only seven Gen 6 titles, making it the second least-represented generation on the list (Gen 5 was dead last, but only because FFVII was the only PS1 game I played that I enjoyed enough to consider among my all-time favorites, and I never owned a Saturn).