I don't use "button masher" as a cheap label for an antiquated genre. I use it in the most literal sense, because this is an iPhone port of Hudson's famous Shooting Watches.
History lesson: Hudson talisman Takahashi Meijin (aka Master Higgins) got kinda famous in the 80's for being able to press a button 16 times a second. Which is pretty awesome. Anyway, to cash in on this, in 1987 Hudson released something called the "Shooting Watch", which let you try and match/beat Meijin's score by calculating how quickly you could press its buttons.