To skip movie cutscenes in the game, delete every file in your \Steam\steamapps\common\Remember Me\ExampleGame\Movies folder, with two exceptions:

Don't delete

BIK_E01_1_NilinFlashback.bik (crashes the game if you delete)

and

BIK_E08_H3O_End.bik (cutscene that plays once the run is over)

This won't skip all, but a good chunk of cutscenes in the game.

If you ever want to restore the cutscenes, just verify your game files in Steam (in Steam, right click on game's name -> Properties -> Verify integrity of game files).

Currently this is the only mod allowed.