Bad design? Fingers can easily latch onto the loop of string at the end of the stick.
Actually, IIRC, the string at the end of the stick is the arming pin, The whole point is that you tie or loop it around your wrist, the pin is pulled and the grenade armed as it leaves your hand.
What happened in that vid is that for this particular grenade, the pin must have been unusually tight, so that plus the inexperience/poor throwing technique of the FNG resulted in the grenade being yanked back a little after release, which caused it to loose almost all forward momentum and fall too short.
As for the lack of protection, well that was a raised position, so had the grenade cleared the rampart at all, it would have fallen out of line of sight and not been able to cause any harm to the users. If the grenade didn't clear the rampart, that was what the ditch was for, but of course, it is probable that the unit did not have flak vests issued. They would have had helmets, but those would not have gone you much good when a grenade drops at your feet.