This is because the CSS for these link nodes (and pretty much everything else from Parsoid CSS) is scoped to .mw-body-content, a class that we set on the main ce.Surface but not on surfaces inside of dialogs.

I tried applying mw-body-content to the surface in the dialog, and that does cause the link node to appear, but it also messes up the font size. Someone with a better understanding of our various layers of font size manipulation (coughtrevorcough) should look at this.

Change 166918 had a related patch set uploaded by Trevor Parscal:
Apply mw-body-content styles to SurfaceWidget

https://gerrit.wikimedia.org/r/166918

Change 166918 merged by jenkins-bot:
Apply mw-body-content styles to SurfaceWidget

https://gerrit.wikimedia.org/r/166918

Verified the fix on test2.

Change 167335 had a related patch set uploaded by Jforrester:
Apply mw-body-content styles to SurfaceWidget

https://gerrit.wikimedia.org/r/167335

Change 167335 merged by jenkins-bot:
Apply mw-body-content styles to SurfaceWidget

https://gerrit.wikimedia.org/r/167335