There are two game modes in Myst Mobile for iOS: Virtual Gamepad Touch Controls, or Legacy Navigation Mode. 

Virtual Gamepad Touch Controls (the default setting) allow use of gamepad-like controls on your device. 

In the attached screenshot there is a "joystick" on-screen. Use this to move forward (up) and backward (down) and to look around (right and left). 

Legacy Navigation Mode enables the single-finger touch interaction to play with your device's screen, similar to older Myst versions. 

You can adjust this choice in the game Settings.