Actually, the very first game I saw on the Amiga (1000) was Nebulus. There was just no graphics in any game like it before that. The school had bought an early A1000 for something like 2000€ (!). With the C1081(?) color monitor and all those colors and smooth movement, twinkly stars, animation... it really outshone every single computer in the school! Sadly, it only had Nebulus and Battle Chess and the Workbench demos to show it off at the time. And of course it was nice, but 2000€ in 1986 meant far and beyond what any kid could hope to own.
Definitive... the reason to get an Amiga... Amiga-Only or excelling on Amiga... well, the reason for me buying an Amiga was the game quality on another computer, the ST
Not one particular game.
Turrican 2 is a good choice, way ahead at the time and absorbing as hell, Amiga-only and pretty early. Exile has stolen the most hours from me
Of the later ones, Worms was way ahead and awesome to play and visually brilliant.