More importantly, it doesn't look _native_ ... to anything really, which is the main (and hard) problem for any portable GUI library.

Modernity can be added on top using a thin layer, if and when needed.

It looks like a native Breeze themed KDE application. If I did not know I was on the Nana website, I would have assumed it's all Breeze.

Modern probably refers to the use of recent c++ standards. (In typical jargon this is termed "modern c++")

I think the modernity is in the code and the API rather than the output

Well, that example shows some too stringy API for my taste.

Ok. I'm not sure what they consider modern in the c++ world

As many words in C++, "modern" is overloaded. In this case I think it means it uses c++11 or later.