How can I get persistent Dictionary popups to go away?
This popover is built into the NSView class (showDefinitionForAttributedString:atPoint:). Since (as far as I can tell) it isn't controlled or powered by a distinct system process, it is completely owned by the app that owns the view where the popover was triggered.

In short, since the popover is owned solely by whatever app triggered it, there's no way to get rid of a stuck one without killing its parent app.

FYI, if the popover isn't dismissed with the escape key or by clicking outside of its body, something has gone wrong. I would file a bug report with the developers of the app where this happens.