It's very difficult to tell from a quick glance through the video, but the usual reason is that the resolution is higher than the targets size leading to decreased range.
As a side note regarding wanting to use the ships that could target without overkill, he could have reduce the # of missile firing tubes on one ship then used the (Assignments) Copy TG button to copy the weapon assignments to other ships in the TG. Then use the (Multi Targets) Same Loc button to fire at numerous different targets in one barrage. Alternatively, if the missiles had adequate active sensors, they could find their own new targets after overkilling.
EDIT- Okay, after a bit of squinting and mashing the HD button, it looks like he has a FC62-R60 using the default nomenclature. I believe that should end up with a 4 million kilometer targeting range or so against a Size 16 target. It would have worked if he was much, much closer.