OK - here’s the technical explanation:
The focus stack has its modal located inside the divs that make the button, this is necessary for the morph effect but it has an unwanted side effect as follows:
z-index is relative to the closest parent that is position relative or static - this is known as the stacking context. Giving an element an enormous z-index when it is inside something with a z-index of 1 will do nothing to bring it to the front of other elements on the page - it is just a layer position relative to other elements that are also inside the z-index: 1 container.
I agree the z-index on the RSSArchitect is ridiculously high but never the less, even if it was much lower, the focus stack would be in behind of it for the reasons mentioned above - i.e. its z-index is meaningless and appears first in the DOM therefore is behind.
The focus stack has a z-index of 300000 on its modal which is utterly pointless as the modal is inside a stacks div with an implicit z-index of auto (i.e. not specified). It will therefore only be in front of itself. You can see a question about it on the original source page of the code (unanswered). Without moving the modal to the body, it is an intractable limitation.
You can fix your demo page with one line of CSS but be aware that if this goes onto a proper page with a fixed menu or other such elements, the focus button could end up in front of them.
z-index wars always end badly and should be avoided.