How does a Touch Screen Digitizer Tester work?
You are asking if this is a legitimate test.  It probably tests many feature. But with out touching the capacitive sensitive surface of the display with a finger, stylus or similar device, I don't see it actually validating all the expected functions of the UUT (Unit Under Test).

As for touch screens, there are many types. I believe you are interested in capacitive touch screens which fault under a variety of circumstances such as wearing gloves, high humidity (due point) and low humidity (static electricity) to name a few.  

added later...


  what could those little boxes with the numbers in them refer to


Guessing, since they are all about the same value &amp; their distribution resembles the expected density of the actual touch screen sensors, they appear to be the raw values reported by each sensor.  If true, this type of test would point out problematic sensors which might be masked by the layers of abstraction software used to improve the user's touch screen experience.