Q: How to describe something that on one level is ironic but on a deeper level is actually extremely apt? For example, I was reading a book on my Kindle last night when this happened:

Of course, counterproductive does not mean "not helpful" but rather "having the opposite of the desired effect" [SOED].  However, in giving this definition, they themselves are being counterproductive by misleading people.  
In their attempt to define counterproductive, they both fail miserably and succeed amazingly.
So, this is some "Inception-level" irony:
1st level) Incorrect definition given by an app feature called "Word Wise".
2nd level) The act of misdefining the term actually defines it quite well through example.
All I know is that my head is spinning and hope someone on this forum could help cure my dizziness.  
Is there a word or phrase to describe this phenomenon?  

A: Irony of Ironies is the term.  This is actually more a quantum physics question than one of grammar. You are looking right at the fact/data (the word) that the interpretation (Wise Words [sic]) fails to interpret. It dutifully brings you the facts as it sees them, though not from the SOED, and does not give you the option to alter or add to its limited data set. Shades of Schrodinger's cat [long dead - deal with it]. I think you are left with Irony of Ironies and that will have to do until the Super Colider is back online.
