The Dark Pictures: Man of Medan follows a similar structure to Until Dawn, where you have a mix of dialogue options, QTEs, and exploration sections. These exploration sections occur less often in the early part of the game after the introduction, but they really start showing up more once you hit the ghost ship. The default character movement animation is somewhat stiff and slow, so you will definitely want to know how to run in the game.
Walking in The Dark Pictures: Man of Medan is handled by moving the left analog stick once you get to the exploration sections. While not always available, you do have a way to move a bit faster to cut down on the time you are walking around with a simple button press.
If you want to speed up the walking speed of the character you are controlling at the time, hold down L1 on PS4 to have them start jogging. Technically, this is not a true running speed you would expect in a game. However, this fast walk is still much better than the default option.
Unlike a lot of games where a run type movie would be used to evade enemies, that is not really the case here for the most part. Instead, this technique is typically relegated to just speeding up your movement itself, as you’re never really running away from enemies outside of cutscenes in Man of Medan.
The one issue you will come across sometimes is that some areas seems to disallow you to run faster, so you’ll just have to judge on whether you’re getting a boost when holding down L1 when moving or not.