The minigame is meant to be a nice break from the point & click gameplay, and to give playful flavour to the scenario. It is supposed to catch the player off-guard, but be immediately understood. We are already playing with turning the phone between a landscape and an inverted landscape screen orientation, so it shouldn't be too much of a change to also add portrait.
The screen orientation isn't actually changed on the fly, even though Unity can do that at runtime; Rather, the gyroscope just gets disabled, and the camera is rotated 90°. Then a scene (scn_03_WorldSwitch_MiniGame) that contains the assets for the minigame gets loaded into the level.