When Eye of Doom enters the battlefield, each player chooses a nonland permanent and puts a fate counter on it. , , Sacrifice Eye of Doom: Destroy each permanent with a fate counter.
By the way, Eye of Fate doesn't use fate counters. A fate counter in Italian would be 'un segnalino fato". This has 'segnalino destino' which seems to be destiny counters. Considering how recent Triad of Fates, localisation errors seem unlikely.