Why was 'structural' chosen to mean 'structural unemployment'?
Cyclical unemployment is named after the business cycle, as in the part of unemployment that varies with the business cycle. Structures are things that last a long time, so structural unemployment is the part of unemployment that is driven by features of the economy, like structures, that last a long time. 

But as you intuit, surely the length, frequency, and other details of business cycles are driven by such structural features. That's almost certainly true, and major reason why structural change and good policy are thought by many to explain the great moderation in business cycles.