Controller is not
required. If a controller is plugged in it may override the keyboard/mouse controls (I don't have a controller so I can't test this.)
The mouse moves the camera, the character moves using WASD
You will see periodically options highlight near the bottom of the screen. (The most common of these are Q
uestion and R
emark.) These are somewhat "Quick Time Events" so they will go away again if you wait too long.
(GoG has labeled this as a point and click adventure but that is not the style of the game.)