What is the definition of taxiing?
Definitions always depend on their context, that is why documents often included a list of definitions. It allows authors to define terms in the context of the document. A definition context is not always a document, it could for example be a field of expertise as well. 

The Commercial Aviation Safety Team / International Civil Aviation Organization (CAST/ICAO) Common Taxonomy Team (CICTT) taxi is defined as:


  The aircraft is moving on the aerodrome surface under its own power
  prior to takeoff or  after landing


More detail can be found in the phase of flight definition document. 
This is definition can be applied in many situations.

The Eurocontrol definition you link to comes from the Air Traffic Flow &amp; Capacity  Management (ATFCM) and Airport Collaborative Decision Making (A-CDM) domains where statistics about gate-to-runway time play an important role for planning purposes.

In that context it is not really interesting to distinguish the time that was spend in pushback from the time spend actually taxiing to the runway. The taxi-out time is hence defined as the time between off-blocks and take-off.