The diversity 'never left'. It just wasn't put out at AAA huge budget levels as it was because the risk isn't worth it for developers.
These games have, and still exist on all levels of devices. It's like people need a game to be sold by Activision and packaged at $59.99 with a pre-order bonus in order for it to be considered a "game". I've played better browser games than a lot of the PS1 games I owned. All the big games that sold back then, for the most part, still have huge sequels today on some system. Miss JRPG's? Get a DS/3DS. Racing games? Everywhere. RPG's? Everywhere from the PC to consoles. Platformers? Skylanders, LEGO, PSP Crash, Ratchet, Banjo Nutz & Bolts, Mario, 3DS games, Fighting? SFIV, BlazBlue, Tekken, MK, and others. FPS? Weren't around as much in PS1, but PS2 and we know how that it is now. Sidescrollers? Tons of Indie that rival PS1 games.
It's a ridiculous statement IMO. The diversity is all around us, it's just not being sold in $59.99 packages and put on a shelf.