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Would it be possible for a beginning piano player (in their late twenties) to learn to play the song (see video) exactly as it's played there, within a year of practice (practicing 30 minutes to an hour every day)?
Nobody can set a timeline for you. That depends on your talent, your commitment, and the quality of your strategies for learning.
I'd say that you can probably learn to perform that piece within a year. To do so with that quality of phrasing and musicality-- that really is up to you.