If characters are different then some characters will always naturally counter others. It's just the way it is in games. Unique aspects counter each other.
Darius does not intentionally counter Nasus. He wasn't released to do that. But Nasus happens to be a scaling (weak early), slow, melee champion with only an attack speed slow, which makes him the perfect prey for Darius, because Nasus can't kite, trade, escape, or fight him. Darius, however, would lose lane to Quinn, because the nature of her kit allows her to kite him, poke him, and vault away when he uses his only engage.
It's just the way it is in any game with significantly different characters. Even card games have counters. Fighting games have counters. Even shooters (at least more complex ones) have counters. And so on.