(...) By observing the two indicator lights, you can see for yourself that, once more, there is a blue-shift - the pulse frequency measured at the receiver is somewhat higher than the frequency with which the pulses are sent out. This time, the distances between subsequent pulses are not affected, but still there is a frequency shift: As the receiver moves towards each pulse, the time until pulse and receiver meet up is shortened. In this particular animation, which has the receiver moving towards the source at one third the speed of the pulses themselves, four pulses are received in the time it takes the source to emit three pulses."
The speed of the light pulses relative to the stationary receiver is:
c = d/t
where d is the distance between subsequent pulses and t is the time until pulse and (stationary) receiver meet up. For the moving receiver, "the time until pulse and receiver meet up is shortened". This means that the speed of the pulses relative to the moving receiver is:
c' = d/t' = c + v
where t' is the time until pulse and moving receiver meet up (t>t') and v is the speed of the receiver relative to the source.
The speed of the pulses (relative to the receiver) does vary with the speed of the receiver, in violation of Einstein's relativity.