given that the melting of the thing could cause ocean levels to rise by up to amost a meter (or even more if it has a cascading effect on other ice masses in the area) that is actually appropriately named.
If you've read the article you will have found the explanation there. The problem isn't the already floating ice, which indeed does not rise the sea level, but the land ice the floating mass is attached to.
Climate change is one contributor to the dynamics of that glacier, so yes it has a lot to do with it, but either way this has nothing to do with your original post, in which you apparently weren't even aware of the fact that the melting of the glacier would rise the sea level which your provided source also states, so I'm glad we have at least made progress on that front.
If an iceberg is already floating in the ocean, then it has already displaced that ocean by an amount.
Just in exactly the same way an ice cube has already displaced surrounding water in a glass.
If or when the aforementioned iceberg melts, there will be no further raising of sea level - because the level was already displaced.
Same as with the ice cube in the glass of water.