Difference between ETA and On-Block time?
The Eurocontrol Lexicon can help here as well. The Estimated In-Block Time is defined as:


  The estimated time that an aircraft will arrive in-block.


(Eurocontrol)

This is not very helpful, but the definition for Actual In-Block Time is:


  The actual date and time when the parking brakes have been engaged at the parking position.


(Eurocontrol)

This time is relevant for gate availability because the aircraft is expected to be at its gate (or remote parking position) at this time.

The Estimated Time of Arrival is, as your quote says, a time where the aircraft is still in the air. This is relevant for Air Traffic Control because the number of aircraft that can fly an instrument approach to the destination airport at the same time is limited. If too many aircraft have a similar estimated time of arrival, some will have to hold in a pattern or are delayed on-route already.