@Sudarshan MG, it depends on the inertial reference frame (IRF). In the IRF of those on the train, the time taken is (L/2)c, as there's no need for them to consider velocity since they are at rest relative to the train. In the IRF of those on the platform, the train is length contracted, and since it's shorter, it will take less time for the light to cover the same distance, but since the train is also moving, you have to factor in the velocity to account for the speed of approach of the light. This results in the equation t = ((L/γ)/2)(c+v) where t is the time it takes for the light to reach the President of Backwardland according to those on the platform. Note that the President of Backwardland is the one sitting toward the front of the train, so we use (c+v). For the President of Forwardland, we use (c-v).

As length contraction is a result of time dilation, I find it somewhat strange that we separately compensate for both length contraction and time dilation.

There is a mistake in the animation at the end of the video because it is not taking into account the time dilation. The animation visualize the synchronization procedure of clocks in team train as seen from the team platform. The clocks at the origin of both frames of reference must coincide at instant T=0 when they are in front of each other, but from that moment on, the clock on the origin of team train should present delay with respect to the clock at the origin of team platform due to time dilation. Instead of that, both clocks remain synchronized, so the animation is not accurate.

The greater the relative speed, the greater the time difference.

something that keeps rummaging through my mind, is this. It always seems that the platform perspective has to be pointing straight forward at the center of the number line. Where as in the physical world to see the other points on the line you have to change that perspective. So I see other factors coming into play, like distance from train, distance from tracks, is the platform located even with train at start of measurement or end or is it arbitrary along the tracks ( or off ).