If an airplane touches down short of the runway, and doesn't reach it, is it still a runway excursion?
It depends.

Skybrary says


  The Runway Excursion category includes also two types of occurrences which do not fit the ICAO ADREP definition for a runway excursion, however considered appropriate for inclusion due to the commonality of a number of causal and contributory factors and/or mitigation approaches:
  
  
  An aircraft attempting a landing touches down in the undershoot area of the designated landing runway within the aerodrome perimeter.
  A runway or taxiway other than the designated one is used for a take off or a landing.
  


My emphasis.



The European Commercial Aviation Safety Team (ECAST) in the European Strategic Safety Initiative (ESSI) use the Skybrary definition when writing about Runway Excursion Prevention


  Articles within the Runway Excursion Category in SKYbrary:
  
  
  Overrun on Take Off
  Overrun on Landing
  Directional Control
  Undershoot on Landing
  Wrong Runway
  


My emphasis.



In an article "Language and safety issues" in Eurocontrol's magazine in 2011, Bert Ruitenberg wrote:


  The whole idea of putting a label such as “runway incursion” or
  “runway excursion” on a safety occurrence is to make it easier to
  file the data from the event somewhere and to compare it with
  similar occurrences. With the definitions above, a take off from a
  taxiway would be considered as a Runway Excursion when the
  Skybrary definition is used, but not with the other RE definitions
  (and rightly so, I say, better label it a “taxiway take off”). Moreover,
  in the ICAO definition, the B777 undershoot at Heathrow
  would not be a RE, but with the Skybrary definition it would be.
  Dear Safety Managers of the world, there still is a lot of work to
  be done...