Well, you
can play with a touchpad, but I would recommend a mouse.
When you hover over a door, a hand icon should appear. When that appears, click and holding down your clicking, drag your finger either forward or backward (depending whether you need to push or pull the door).
If you still have problems, run the game, walk up to that door and then just exit the game.
Once so, could you tell us where you got the game from, and post the hpl.log file.
Since it appears you're on a Macbook, you should be able to find this file at this directory:
~/Library/Application Support/Frictional Games/Amnesia/Main
This will help us better understand your computer hardware and software setup, as well as give an idea as to what is happening in the map itself.