You have to understand how far opening knowledge has advanced. Things that are clear to us were almost unknown to players of the 1920s and a bit fuzzy even to the best players in the 50-60s. I remembered being very surprised at the handling of the Queen's Gambit in the Capablanca - Alekhine match - they were playing moves that are clearly not the best to our eyes, yet they were going for them, and even repeating them, and not criticizing them in later comments. Overall they were playing completely harmless lines that were lacking ambition both for White and (especially) for Black.
In 1956 the King's Indian was trendy and the Grünfeld was not. Nobody thought it was worth avoiding the Grünfeld. Even 40 years later Kasparov struggled many times against Karpov and Kramnik. The Grünfeld as a feared opening because it's a direct attempt to draw by force is a product of the computer era.
Let's also not forget Fischer was still 13 at the time of this game. He did not have the knowledge and mass of opening work he had later.
The strategy of playing 1. Nf3 to transpose into some 1. d4 openings while avoiding some others and/or keeping the option of using the d pawn differently only really came into full strength with Kramnik's White repertoire of the 90s. It was initiated by Botvinnik in the 40-50s but Nimzos and Grünfeld were not as feared back them.
I know the first five moves of the so-called Game of the Century (Byrne-Fischer, 1956) are probably the least interesting thing about it, but they do puzzle me. These days, anyway, starting with Nf3 is nearly always an attempt to avoid the Gruenfeld. So why does Byrne start with 1. Nf3 . . . and then allow a Gruenfeld? In 1956 were there different ideas prevalent about how to handle these move orders? Was this a standard order at the time, and if so, what was it for? Or was it a head-scratcher even then?
Is 5. Bf4 some sort of attempt to play in some new way against a King's Indian or something like that? It seems like it would be bad against a KID (since Black surely gets in e5, and now with tempo). So I'm somewhat further puzzled by why Fischer didn't play 5 ... d6 (it's not like the KID wasn't familiar to him...). It looks like this game was actually Fischer's first ever Gruenfeld. Why did he play it at a moment the KID looks so much more natural?