Perspective 2D image as texture on 3D object

Hi.
I want to make an adventure game in the style of Broken Sword 5 - Serpent’s Curse or Whispered Worlds 2.
The latter is a bit trickier. The main thing is, that the whole scene is painted/drawn in 2D and then it is turned into a 3D scene ( Broken Sword 5 may not do exactly do this, but Whispered World 2 does ).
Take a look at the following screenshot of Broken Sword 5: http://guides.gamepressure.com/brokenswordtheserpentscurse/gfx/word/75390915.jpg
You see the character standing in front of a desk ( the characters are 3D and therefore the scene has to be turned in to a 3D scene because otherwise there will be problems with things drawn in front of something else when they shouldn’t. ).
I want to recreate that scene to learn how it’s done.
I cut out an image of the right side of the desk: http://abload.de/img/desk_side9lkax.png
The 2D scene was of course created with perspective in mind. But how I can use this (perspective) image as a texture for the right side of a block, that I created in blender?
I tried to unwrap the block and tried matching the UVs with the corners of the cut out image, but the result doesn’t look right. Here is what I mean:
http://abload.de/img/desk_uv_wrong0xjt1.png

I also found a making of video of Whispered Worlds 2, I think however that they are using Cinema 4D, don’t know how texturing/uv unwrapping works there:

Any help on how I can achieve this in blender is appreciated.

https://docs.blender.org/manual/en/dev/modeling/modifiers/modify/uv_project.html

This modifier changes the default uv map of the object. You only need to peek the camera as the projector, and if needed scale and position the image into your scene.