Right. Yes, I think it's wrong. You can "give up ....ing", meaning "stop ....ing" e.g "give up studying French", but in this sentence the meaning is "to stop thinking something is going to succeed" where you should use "give up on", e.g "I think I'll have to give up on the idea that I'll ever be fluent in Japanese"
I have to say a lot of the sentences in that dictionary sound a bit odd, not sentences that a native speaker would use or have said. There are also a few places where commas have been singly used so I wouldn't trust it completely.