Are you sure about that? I can possibly see a state transition going that fast here and there, but you do realize it would take a sustained 70 presses per second to see a button down every 14ms? Sorry but that is not physically possible, although perhaps you can induce it here and there with some crazy all-knuckles button-mashing, and maybe there is even some bounce in the hardware itself. Have you ever watched a video of professional StarCraft players, where they use all the fingers on one hand plus a mouse and click so fast it's a blur? Those guys are gods if they can do 300 actions per minute which is 5 per second using both hands...
That said, in general with a lot of games you just see input polled every frame. The possibility of an entire press-release-press happening within a frame and getting lost is pretty remote at interactive framerates, and I have never known a game developer to worry about this.
On some systems you may get buffered input. The system monitors the input devices asynchronously and fills up a queue with all the state changes that took place since the last query, and generally you would let the buffer fill up between frames and process it each frame, so the resolution may be higher than polling the state each frame.
Some systems are event driven, so you can register a callback that fires every time input state changes, although the resolution will be dependent on the rest of the software stack and may or may not be significantly better than a per-frame check. For example if the API is just polling the hardware every frame, comparing it to the last frame and then firing the applicable callbacks, you aren't doing any better.
With embedded systems and some old game systems that were programmed to the metal, you would have had interrupts for the buttons. An interrupt is a little piece of code you register with the system that runs every time something happens. In the case of a button interrupt, the hardware would be physically designed so that when the voltage on the wire connected to the button goes from low to high or high to low, it runs this bit of code. This would be the most direct and responsive system but most games these days have a ton of hardware and software between you and the buttons.