I've never played Machinarium on a touchscreen, so this is just a guess:
instead of "tapping" the book to activate the animation of turning pages you may need to tap~hold~swipe, like if you had a physical book open in front of you and were turning the pages with your index finger. Tapping & holding is the same technique you'll eventually have to use to turn cranks, pedal gizmos, and press seeds later in the game.