Is the Rubin Vase illusion an example of inattentional blindness? Generally, people looking at an example of a Rubin Vase see either the vase, or the faces. The brain seems to make a decision on which one is being viewed, but both cannot be focused-on at the same time. 

Is the Rubin vase a form of inattentional blindness, caused by the same brain function that only allows us to focus on certain objects in our field-of-view, but not others? The Gorilla-in-the-Room is another example.
Short answer
The Rubin Vase is a visual illusion, which can be traced down to the way the visual system analyzes visual scenes in terms of objects and background. Inattentional blindness is not an illusion, it is the failure to detect stimuli when the mind is focused on something else. It has to do with the limitations in the capacity of the visual system to extract relevant information from a visual scene.

Background  


The Rubin Vase illusion (Fig. 1) is an example of an ambiguous figure/ground illusion. The visual system interprets patterns in terms of external objects. To do this, the visual system distinguishes objects (figure) from background (ground). In the Rubin Vase illusion, when the faces are considered background, you will see the vase as figure, and vice versa. 



Fig. 1. Rubin vase illusion. source: TU Dresden 

The visual system represents objects primarily in terms of their contours. Also, elements that are close together, or share certain features, or are homogeneous in certain respects tend to be grouped together (grouping). The sudden reversal one may perceive is thought to be due to a shift of attention on the shape of the contour. The observer's "perceptual set" and individual interests can also bias the situation. Biasing the shapes or contours can make one interpretation stronger than the other one. This particular illusion involves higher cortical processing, because previously stored information about vases and faces are resourced (source: TU Dresden).


The Invisible Gorilla (see a video clip here) (Fig. 2) is the effect where people instructed to focus on a particular target are prone to miss other salient, sometimes striking stimuli. The classic, familiar example being subjects shown a basketball game and they are instructed to keep count of how many times the ball is passed between players in the black team. When the subjects watch the video clip and attentively count the number of passes, about half of the subjects totally miss the scene in the video where a man in a giant gorilla suit walks slowly into the middle of the screen, beats his chest and then wanders off, because they were so focused on counting the passes (that’s not to mention the other deliberate mistakes in the video) (source: Life in the Fast Lane). A newer version hits home even harder; 24 experienced radiologists were asked to perform a familiar lung-nodule detection task. A gorilla, 48 times the size of the average nodule, was inserted in the last case that was presented. Eighty-three percent of the radiologists did not see the gorilla. Eye tracking revealed that the majority of those who missed the gorilla looked directly at its location. Thus, even expert searchers, operating in their domain of expertise, are vulnerable to inattentional blindness (Drew et al.,, 2013).



Fig. 2. Invisible Gorilla. source: Persuasion Blog

The Invisible Gorilla is an example of inattentional blindness. Inattentional blindness can be defined as: 


  The failure to notice unexpected objects or events when attention is focused elsewhere [...] (source: Simons).


Reference
- Drew et al., Psychological Science (2013); 24(9): 1848–53