I finally managed to play it with a proper camera.
Seems like the problem occurs only if you Alt+Tab and come back to the game. You mouse cursor becomes able to leave the game screen. While it's outside, the game doesn't pick up mouse inputs.
So, as long as the player doesn't interrupt the game, he's gonna be fine) But, I guess, some people would do it just like me, so they can make a screenshot of the right path in the starting room.