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Nintendo's treatment of third parties as well as their decision to go with cartridges doomed them.
They had the best hardware (ps1 graphics looked like crap compared to n64 graphics, as soon as mario 64 came out ps1 graphics felt like last gen), they had four player built in which at the time was incredible and they backed it up with AMAZING multiplayer games which made n64 THE party console, it had, other than rpgs, hands down the best top lineup of games of the gen.
Not to say ps1 didn't have plenty of great games, but the top 10 or so games for ps1 was basically rpgs and metal gear solid. The thing is, ps1 is when rpgs, and especially final fantasy, were in their heyday in terms of popularity. The snes square rpgs are some of my top games ever, if it wasn't for them i wouldn't consider the snes to have the best library of all time. Coming off their increasing popularity, and with the introduction of 3D, rpgs and especially final fantasy just exploded and have never been as popular before or since. I wanted a ps1 solely to play square games - there were other good games but that was the bullet in nintendo's side and as an n64 owner it was painful to miss out on that. Plus the mix of still really popular 2d fighting games from the 16 bit days and the new novelty of 3d fighting games (which turned out to not be a good genre but at the time people were interested cuz it was new) also hurt n64 badly since they only had a couple good fighting games.
If nintendo had been nicer to third parties and gone with CDs, they would have kept all the jrpg's that got popular on the snes and would have had much more third party support, cheaper games, no ridiculous game droughts or complete lack of genres like rpgs (Quest 64 anyone? haha) and likely ps1 sales and n64 sales would have been reversed. ps1 had nothing to match nintendo's first party forays into 3d with n64, but the thing is ps1 had everything else while the n64 got huge game droughts.
But as we all know, nintendo did as they so often do, and just royally screwed themselves (we're seeing it still now 20 years later with discontinuing NES Classic, just horrible business ideas), they had their standard F#$% You attitude to third parties and went with the more expensive less capacity software medium, got hardly any games.
The OP's graph shows everything you need to know, ps1 was nothing special and didn't have much in the way of great games, n64 came along and had huge initial sales (mario 64 blew away everything on the playstation), then ff7 hit, momentum shifted, and it was all over.
With the n64 they showed the industry how to make incredible 3D games, how to make 4 player absolutely necessary - the first party console, introduced rumble, introduced the analog stick, still has some of the very best games every made, and f#$%ed up everything else.
