How Einstein Abused Logic in 1905

Einstein's 1905 conclusion: The moving clock is slow, the stationary one is fast:

https://youtu.be/Q1y3YnPgaY4?t=1157

Albert Einstein, On the Electrodynamics of Moving Bodies, 1905: "From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by tv^2/2c^2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B." http://www.fourmilab.ch/etexts/einstein/specrel/www/

Does this asymmetric time dilation validly follow from Einstein's 1905 two postulates or is it just non sequitur?

Pentcho Valev