I would agree with the more extended outlook on how much time it takes. The game could be looked at in a disjointed way. In reality, you don't move then shoot. You may do both at once and the phases are a simplification for rules' sake. Turn 1 would take longer in real life as you move to positions, scout enemy movements and maybe engage in a small firefight. But as the battle progresses and you know where your enemy is things speed up. You no longer need stalk through cover but want to engage at this point. And there we must break from the convention of modern warfare. I mean no disrespect to soldiers but they are not as inclined to fight melee as in historical battles. 40K is more akin to this begone era of muskets and swords. So a pure ranged engagement does take longer but not by much.
Lastly, while those intro videos are awesome they cannot represent turns or phases. As said above the phases are an abstract concept and cannot be applied to real life. You can even see in the second video especially, both sides are moving, shooting and charging simultaneously. But the videos do show the skirmish nature, lasting briefly while other battles could be occurring elsewhere. Remember from history that a single battle could last days with multiple engagements, firefights and lulls occurring over large areas between multiple autonomous regiments, divisions or patrols, etc. A single encounter could be only an hour or several depending on the composition and disposition of those involved.
"Fetch me another plaything. This one seems to have broken." -Urien Rakarth
Space Marine- "This planet is ours, witch."
Eldar- "No ... This planet is theirs ..."