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Sorry, but I don't know why this sounds contradictory to what is stated on the post.

New economy enables people to take away rewards from others with downvote. A vote reward is only claimable after 7 days, and will stop generating rewards after that.

To me it sounds like after 7 days one cannot earn from their video, is that what the last statement means?

It means that rewards are not claimable before 7 days. After 7 days you can claim whenever you want and it will continue to earn rewards if you don't click claim. This 7 day added to prevent future reward pool abuses.

And after claiming, it won't get rewards anymore? Sorry, I'm having trouble understanding when the rewards will stop exactly.

Is this implemented to recognise an abuse pool during that period and being able to downvote to remove the rewards?