16 "buttons" is what we have on current gen console controllers. The 360 has four shoulder buttons, A, B, X, Y, D-pad, start, select and click functionality on both analogue sticks. Some games (GTA V) come close to using all of them.
Yeah. In the typical twin-stick usage, this thing is missing one button on each side - it's got an extra shoulder button on each side (the ones on the back) but in the place of the 4 right face buttons and the left D-pad it's got 2 face buttons on each side.
Realistically, the other 4 buttons (the 3 bars on the bottom and the touch-screen) don't map to normal gameplay buttons, whereas a Sony/XBox gamepad will only have two of those "non-gameplay" buttons.
So technically, this thing has 2 fewer "gameplay buttons" than a typical controller. But it has a touchscreen, and you can put a lot of the low-reflexes stuff in there.
