Is it KLM, or just the KLM flights operated by Delta (of which there are a decent chunk)?

Sounds like it's a majority of KLM flights, so seemingly it's themselves.

KLM was flying, but all flights pass through Schiphol Airport (it's their hub) and Schiphol couldn't board fights for a while. Because of that they ran out of gates for arriving flights, so everyone had to cancel flights to avoid compounding delays. As the biggest user of Schiphol that means KLM had to cancel a lot of flights.