So the main point of the article would be "computers can not have consciousness because they just compute. They don't have feelings as we do". Correct?

I think this argument is too simple. Looking into our brain, we see exactly that: computing. Nerve cells get excited (1) or not (0) based on the signals they get from other nerve cells. As far as I know, we still don't know, where consciousness or feeling starts, but it does have a lot to do with the algorithmic behaviour of nerve cells, right? Doesn't seem too far a stretch to think that it is less about the fact, whether we use organic tissue or transistors for building consciousness. And more about the way, the entire system is build and parts are linked with one another.

I intuitively think that your claim is true but I think your argument doesn't work.

The author would say that "for everything conscious there is a body underlying it". In most of the cases this is (most of) our brain. But that isn't the same as to say that "For every body part: there is a consciousness based on it". Having our legs removed doesn't change our ability to have what the author calls "landscape of joy" or processing feelings.

What you describe is an error in perception of something. The person is still conscious though, as you describe yourself. Conscious of something that isn't there, but nevertheless conscious.