While not narratively crisis like, it was certainly a crisis that changed DC (imo for the worse) as much as any other. It ushered in the ultra grimdark theme change for DC, even moreso than the 90s ever did.
I think people are too hung up on "It has to involve multiversal stuff!" because that typecasts DC's most major events into one very, very narrow style of storytelling. Identity Crisis is certainly included in DC's own official list and if they don't decide what counts, who does? Just because the first Crisis was like that doesn't mean the others have to be. It's like saying every Superman story has to be like AC #1.