With the release of the PSX, Sony gained the majority of the gaming market, using many methods to secure their spot as #1. Up until now, the majority of the gaming market have been clinging to the Playstation - which explains why Sony's hardware/software outsold Nintendo and Microsoft sales combined - but now, people are becoming interested in Nintendo's line up of games. This is what is meant by the 'long renaissance', and suggests that Nintendo are going to claim position number 1 in the console war, thus putting 'recent demons' (Sony) to rest.
As for Nintendo not doing anything real special:
Great games: They have many quality titles that people are becoming more interested in. They don't have online games, but they have great multiplayer games. Online games has never been what console gaming is about anyway. Besides, it still hasn't really taken off, and is not needed to outsell other systems.
Low Prices: People are now grabbing cheap Gamecubes. There was an article saying that Nintendo had sold the most units on any one day, since the last 20 years. This has worked out quite well for Nintendo aswell, since it costs them far less to make a Gamecube than it costs Sony and Microsoft to manufacture their systems. Before the price dops, Sony and Microsoft had been loosing money of every unit sold, and Nintendo was breaking even or making a small profit. Now Sony and Microsoft are having to lower the prices for their systems even more to compete with the price drops of the Gamecube, so they loose even more money on each system sold. But Sony argues that anyone who wants a PS2 has already bought one by now.
And speaking of doing anything real special: What did Sony do with the PS2 to claim #1 in the 128-bit console war? Nothing! All the support they had for the PSX just 'upgraded' and bought a PS2. They were basically #1 the day they released the PS2.
It's not like they saturated the market with ever-popular on-line games, took lead of the console race, or did anything real special.
What I'm getting at is that you don't have to do any of this to sell lots of units, or outsell other competitors.
