The important aspects that creates "unnecessary" prolonged engagement -
1. Unnecessary - a befitting word - keeping in context that one would love progression, but this game sometimes loops back to previous levels because of uncanny differences on "strike" & "impact" and prolonged engaged at one level - with multiple attempts due to positive addiction behavior
2. Subtle "Strike" and "Impact" [self-coined words] of the birds at various "points" (areas of impact) of the structure or opponent territory - provides different down-fall and dismantle of the structure
3. When there exist variation in hit/strike "points"; "Let me see how if it would work if falls on this particular point?" is a differentiated attitude/behavioral modal that emerges either planned or through serendipity means
4. How can you get three stars or higher points by utilizing less resources to destruct the opponent Pig sty/structure
5. Tend to give another worth try as a means to find a mode of attack in variance of swing, direction or through trajectory - once again planned or by casual serendipity
6. Learn about structural dynamics, look-out collapsing details of the structure - capture and utilize it in the next attempt as a key driver
I feel that the addictive game-play is also through assuage of attack, destruction which is more an easy exercise than building - which in itself is different behavioral attribute. It feels easy to do - easy to cling on and improvise. One thing for sure your target may miss - but its worth a try, that the object creates some form of down-fall; smaller successes to build initially.
Angry Birds calls itself in marketing notes as a challenging physics-based demolition gameplay, and lots of replay value.The certain appreciation of replay is what creates that addiction and "unncessary" mania in a prolonged manner - where progression in gameplay is not always the end but strange looping-back mode to previous levels is to be noted.