Seems like the Dash dev disagrees with the icon author on where the line between "inspiration" and "plagiarism" lies. It doesn't help that there's a language barrier between the icon author and Dash developer.
But sadly it seems like this issue hasn't been rectified, but has just been forgotten about. I only found out about this after I'd bought a license; I'm posting this here in case someone else finds it relevant to their purchasing decisions.
I'm not familiar with the controversy besides what you posted, but my take away is that icon dev has some talent. The bookcase D is clever and well done, at least at that size.
In the link for the alternative icon, the icon designer has declined to enter any new discussions, as he felt "insulted" with the Dash developer's reactions on Twitter. He feels any more discussion is "a waste of time."
At any rate, I wish we non-Mac users had something like Dash.
In the interests of quoting the full context rather than just a few words, here's what he said in full:
"Dear The Great Developer of "Dash.app".
I do not ask you anymore.
I do not say anything about your icon.
It's a waste of time.
But I am vindictive.
Conversely, I inspired from your icon.
This is the way of my protest.
This time, you do not plagiarize this my icon, please.
Sayonara さよなら."
It seems the designer is Japanese, so there might be a language/cultural barrier too, but for what it's worth I think I would feel insulted by the Dash developer's reactions too!
Not to mention you can import and make your own DocSets, can integrate it with Xcode and much more. If you're developing anything on a Mac, you should probably have this installed (and pay to support it of course).
It's also a snippet manager, though I don't think many people use it for that purpose.
I love Dash, it's saved my butt when I've had spotty or zero Internet access. However, I've found that on my laptop it is far faster to do a web search for documentation than it is for Dash to do the search locally.
Very simliar goal, but offline and instant. After using it for a while it's hard to imagine going back to reading documentation in a web-browser.