If Google removes public information, it's a loss for everyone. If they don't, they're immediately open to a legal battle.
This is just a horribly rash, poorly thought out law that has little to do with actual privacy, and more to pushing the problem on to Google and their ilk.
How is it any different when individuals work for the state? Couldn't government entities just submit complaints on behalf of their employees? Hell, why wouldn't the government just have employees have to sign a form allowing for the government to send out blanket complaints to Google every month to remove information related to them or their work?
They like to pretend that those decisions are somehow unimpeachable because they're made by an algorithm instead of directly by a human, but the algorithm is still written and adjusted by humans.
The law defines the right, it doesn't force Google to do anything. Google can take every request to court.
The qualification "horribly rash, poorly thought" out applies to the services Google creates ("huh, privacy, what privacy?"), and the way it responds to request to comply with basic privacy ("fuck you, fuck you and fuck you, oh, oops, we lost in court, let's hack something together to prevent losing $$$").
Besides, Google already decides. There's nothing even remotely objective about Google's search results, and Google is eager to pro-actively censor it's services for anything ranging from the copyright mafia to American puritanism.
The EU lawmakers didn't force Google to be a bunch of assholes. They just defined basic civil rights.