I LOVE this music video! It combines two of my favorite games and is just a great animation in general. The song is amazing and I have it saved as one of my favorites. (And yes, I'm aware it's missing the potato and some other key Portal elements! The animators weren't perfect!)
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The reason why it didn't include some Portal role elements is just because Cubical guys couldn't fit everything in a short music video. I've seen similar thing with World Of Gray animation. So it's not their imperfection, and it's not a retell of the lore, it's just animation for the song.
Yeah, I understand. Plus, there was also the audience that would be seeing this video that had never played Portal before, so they wouldn't understand that, oh, that potato is the same character as that giant robot! So there was the whole making-it-easier-to-understand piece, too.