Being successfully might not mean being at the top of the pyramid. DDG is a an example of a successful search engine.

Further, they don't have to be better than google in the quality of their search results. As soon as the results have good relevance, it's good competition.

What matters is that they are 'good enough', that there is a hint of competition to the Google-Bing monopoly. Offering privacy centric 'competition' is what they say their main aim is and what their success should be judged upon.