There are two kinds of "execute" abilities. It either refers to those abilities that deal true damage and are guaranteed to kill targets below their threshold, or abilities that simply do more damage the lower the target's health. Garen's is the latter.
Pyke, Cho'gath, and Urgot show an indicator because it is guaranteed the enemy will die if the ability hits them.
Darius's indicator is for max stacks of his passive. It doesn't mean your ult will kill the enemy.
Evelynn's indicator only means it'll double the magic damage she deals to the target. Someone with enough MR or HP won't die even to twice her ult's damage.
Garen only has an indicator when his ult will deal true damage, because that enemy is the Villain. And it would go against that thematic to allow it to reset. Someone's the villain because they have the most recent kills. Once that target's dead, it wouldn't be justice to just kill everyone associated with them.
It'd also be pretty difficult to program such an indicator, because Garen's ultimate is technically infinitely scaling. It deals damage based on a percent of the target's missing HP, so it'd have to do extra math.