Why does a change in excitation of an alternator affect only kVA and not kW?
Think about the phasor diagrams as differences.  If E1 = E2, then Er = 0.
A synchronous machine can work as a generator or motor.  Used as an alternator (generator), the synchronous machine is driven by a prime mover.  Once synchronized, prime mover controls real power (kW) and excitation controls reactive power (kVAR).
If you take two alternators (synchronous machines) (same size) in parallel and synchronize them (same voltage, frequency and phase sequence), the two alternators should balance the load between them (same kW, same kVAR, same current and same power factor).  Reactive powers may require adjustment for balancing.
Power from the two alternators goes to the load.  Think of two ox yoked together.  Both can only go at the speed of the other.
The load does not change (constant).  It requires the same kW, kVAR, current and power factor.
The page (and the previous page) discusses the impact of changes in the alternators if something changes in one of the alternators.
Previous page deals with a decrease in voltage E1.  There is a difference in potential between the two alternators.  E1 decelerates.  E2 starts to drive E1 (supplies power) as a motor.  E2 accelerates, which pulls E1 back into synchronization.  Higher potential attempts to charge lower potential.  It is called motoring and worse case scenario, breakers on E1 (motoring) and/or E2 (over-current) trip.
This page refers to a decrease in excitation.  The excitation controls reactive power kVAR delivered to load.  The real power kW will be equal for both alternators.  If alternator 1 decreases kVAR (lags), then alternator 2 must increase kVAR (leads) to supply constant load. The kVA (apparent power) and kVAR for both alternators change, but the kW (which come from prime movers) remain the same.

The text you reference works.  Shipboard Electrical Power Systems by Patel is a good reference.  The marine system is a complete power system, so is a good source of information.
If the load is constant, the sources must supply a load proportional to it's ratings.  Say a 2MW generator and a 1 MW generator (driven by diesel engines as prime movers).  If one is at 50% the other will be at 50% (1MW + 500kW) (50% of proportional kW, kVAR, current &amp; pf).  The ox analogy.
Now if the larger decreases to 900kW, the smaller increases to 600kW (1.5MW), but actually &gt;600kW since the difference in induced voltage changes and smaller generator attempts to drive (motoring) the larger (the sychronizing current), which should bring both into sychronization.
In this case kVAR from each generator does not change, but kW, current and power factor change if the load is constant.