PS1 would still win. But N64 would sell at least SNES numbers, and PS1 would sell around 80 million or so.
Square Enix would stick with Nintendo. Maybe they would release Final Fantasy VII at some point on PS1, but not at the same time as the N64. Capcom and Konami would likely be more dedicated to Nintendo, but also tip their toes into the PS1 if possible.
The Nintendo 64 DD would no longer need to exist, but the Randnet cart would still be made. I don't know if it would release outside of Japan though. Hopefully the N64 would play audio CDs like the PS1 did.
Animal Crossing may have made it to the Nintendo 64 worldwide, considering the install base would be bigger than it was in reality.
Lifetime Sales Predictions
PS4: 122 mil (was 100 million) Xbox One: 55 mil (was 50 mil) Switch: 79 million
3DS: 77 mil (was 73 million)
"Let go your earthly tether, enter the void, empty and become wind." - Guru Laghima