I don't know what an "interpretation video" is, but covers are clearly copyright infringement.
The first question to ask is: does audio deserve copyright at all? I think the answer to most people is yes: audio is just as valid a medium for fixation [1] as writing.
In that case, it's pretty obvious that a cover violates the copyright of the song writer.
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I think it's immoral and should be illegal to distribute others people work without permission but I think it should be perfectly legal to make art based on work of others as long as you don't use original samples (it's fine to make a cover, not fine to use original soundtrack).
The same goes for software: distributing what others make is wrong and should be illegal. Making something similar yourself? Fine, go ahead with it.
Why do you think the soundtrack should be protected, but the lyrics shouldn't be?
If you're doing it "similarly" after knowing the original, isn't that just "copy my homework, but change it a bit so the teacher won't notice"? In that case, why provide copyright in the first place?
The same goes for audio, I guess. If my (potentially perfect) recreation of your song is allowed, why bother protecting it in the first place?