There's an interesting thing in that the sales numbers and the narratives differed strongly in that generation.
The Gamecube, while having sales nearly equal to the original XBox, is beloved mostly in retrospect; at the time of release the consensus between North American enthusiast press and corporate PR swung strongly in favor of "grown up" games(i.e. 90's edginess with swearing, gore, and boob) while Nintendo was still making "kiddie" stuff. Of course, plenty of folks bought Nintendo's offering anyway, but it wasn't clear what their strategy was at that point. They gained their now-standard reluctance to push graphics tech further on consoles with the Gamecube; it was a well-rounded game player, straightforward enough to develop for, and not hugely different from the others in spec, but it avoided doing really flashy graphics demos. And for the press, who had gotten used to talking about how high tech and advanced every release was, and how big the production budgets were, this was an affront. If you make smaller games with less graphics that aren't for the reviewer's specific demographic, their job is harder and needs more nuance.
And so while the larger side of the market aided and abetted a "gamer" image, which was really just catering to whomever would give them more coverage - Nintendo stuck to its own plan. It could afford to; every portable system was a hit. So they started making their consoles more like their portables after the missteps of the N64(which was a graphics beast, but too hard for most developers to delve deep into).
The reality, of course, was that the GCN quickly became a fixture in college dorms because it had good party games like Smash and the Mario Kart series. It was there right along with the PS2 and XBox and their exclusives, and
yet when you saw interviews with game industry producers and the like, nobody at the time said "we should be more like Nintendo". They wanted a GTA or a first-person shooter with better lighting effects. And there was a xenophobic "beat Japan" angle among some in favoring Microsoft over Sony or Nintendo. In effect, they gaslit some part of the gaming audience in order to push the type of games they were making and the country that games should come from. It was only later in the 2000's with the next generation releases that critical backlash against the "grey/brown shooter" arose and Nintendo's position was championed - though not by everyone.