I read through the paper, but couldn't find any description of what the brain does which couldn't be considered information processing. It may not be digital processing, and it may not resemble how computers process instructions and retrieve data, but even if the physical architecture is different the brain still seems to be processing information.
He uses an example of a dollar bill, and how a person cannot recall every detail of a dollar bill from memory if asked to draw one. And that is somehow proof that the brain does not store data about the dollar bill? The person was still able to draw some details about the dollar bill, such as a person in the center and the numbers in the corners, so that data was stored somewhere. The author also makes a silly distinction between "storing data" and "changing the brain", as if the way the brain is changed isn't how it stores the data.
But neither the song nor the poem has been ‘stored’ in it. The brain has simply changed in an orderly way that now allows us to sing the song or recite the poem under certain conditions.
Sounds a lot like the brain stored the song or poem somewhere in a way it could be retrieved later, under certain conditions. Just because the brain stores information in a less precise way as a computer doesn't mean it isn't storing anything. The rest of the article continues to make similarly odd claims without backing them up. The researcher takes some very valid arguments about how many researchers rely too heavily on computer / human brain metaphors, but then he makes a lot of wild statements himself without backing them up either.