As you can see in the photo below, he's got some fantastic taste - with gems like The Legend of Zelda: Ocarina of Time on display, Rare's GoldenEye 007, and what appears to be the original Paper Mario game. We can also see Blast Corps and Conker's Bad Fur Day. Outside of the container you can also see games like Majora's Mask, Resident Evil 2 and Jet Force Gemini.
Although Reggie was a big gamer before joining Nintendo, he did admit he didn't actually own a GameCube when he originally applied for a job at the company. Up until that stage though, he had systems like the N64, PlayStation 2 and Xbox. He also had quite a large SNES collection, made up of "over 80 games".
If you are keen to relive any of the above-mentioned N64 titles, or any of Nintendo's other retro game libraries, you can always subscribe to the company's Switch Online + Expansion service. It contains all sorts of games, with new titles added on a regular basis.