This is a technique called Tilt Shift Photography. It can be performed entirely using optical techniques or using software to post process an image.
A lens with tilt and shift capabilities allows you to more selectively control which parts of the image are in focus, and the plane of focus.
It can be used to make more of the image than normal be in focus, or it can be used to very selectively focus only part of an image. When used to create a shallow depth of field it tends to give an impression of the image being of a miniature model - so called miniature faking or diorama effect.
As @barbeque stated in a comment, the theory for why the brain interprets these as miniatures is that the depth of field resembles what the eye sees when focusing on a very close object. When we focus at a distance, the depth of field we see is very much larger, so we don't see the kind of blurring that we see in these tilt-shift images.
The following is a still picture example of the technique.
By Phpcitizen - Own work, CC BY-SA 3.0, Link
I couldn't find a reference to precisely how they did this in Game Night, whether this was entirely camera-work or post-processed images. Now that you know the name of the technique, you can see this mentioned in lots of reviews of the movie.