All four of the links show up in the read view, but when you open the page in the visual editor, two of them are completely invisible (though not destroyed). Both of them omit the project code (e.g. [[en:Barack Obama]]), relying on the fact that this default to Wikipedia.
Looks like the siteconfig api response (https://meta.wikimedia.org/w/api.php?action=query&meta=siteinfo&siprop=namespaces|namespacealiases|magicwords|functionhooks|extensiontags|general|interwikimap|languages|protocols|specialpagealiases) doesn't provide this info.
So, we'll need to push a patch to core to fix this there before using this info in Parsoid.