Firstly it's completely false that you can't set DDG as the search engine in Android Chrome. I just did it. Here's how:
1. You visit DuckDuckGo in mobile Chrome.
2. Instructions from DDG pop up on the screen telling you how to find the default search engine picker screen (you click settings, and search engine is the first setting on the screen, so this is not hard).
3. DDG is now an option I can pick under the "recently visited" section, which is clearly visible on screen.
The search engine screen has Bing, Ask Jeeves and a few others pre-bundled, so perhaps they're salty because they aren't pre-bundled. Or perhaps the current behaviour wasn't always true in the past. But even if that was the case, it's fine today, so why are they complaining?
As for owning duck.com what a stupid complaint. DDG chose an awkward name for their search engine and own the domain name for it. They are not called and do not own the name "duck". If they want a short single word .com domain they can always rebrand. Google owns lots of random seeming domain names, but there's nothing wrong with that.