Though it may sound unscientific as an answer, people get addicted to flappy bird because I'm an older person now. This answer is in fact quite the summary of a rather long series of rants, accusations, and zealous narrow-mindedness of myself, which are; despite being what ther are, all justified (in my universe (which is the one true ultimate universe (which makes this answer completely obsolote.)))
A rather more elaborate and rational looking answer I would give (which would still be unacceptable by majority, though) is that it is not people who are addicted to such games, but populations. Today, a significant percentage of people have access to mobile devices - which can also be used as gaming devices - and thus most people play games. Those of us who remember that only a small percentage of population had access to computers (the major gaming device) and even a smaller percentage of these people used to play games are daunted by this small fact. Whereas in the past a small, intellectually developed and capable population could play games (and thus games were made according to that appetite) today intellectually undeveloped people (a large chunk of the bell curve) are tha majority of the players and thus games are made according to their appetite. BUT only OLD people like me think this way (and don't care about the seemingly humanitarian but ultimately futile flamin replies to such an explanation) think this way... So... there you go... I feel lighter...
(There is still more inside, wanting to rant about quick time events, rapidly pressing x to climb ladders, extremely dumb games and games that are difficult just for the sake of being difficult instead of being challenging for marketing reasons but... this will have to do for now...)