To hit someone in the eye, you've got to aim at their eye and land a round there. That is, accuracy at hitting a pre-specified target.
To hit armour in the same location twice, you need either two (or more rounds) delivered consistently on whatever happens to be where the first round lands. It's a case where being a Texas Sharpshooter actually works (painting bullseyes around the bullet holes you just shot into a barn).
A compound impactor with a leading and secondary round might work, for example. Difficult to package into a small-arms round, but possible. Keeping everything on the same impact point would be the crucial element.
At that point, wouldn't it be easier and just as effective to use a single, larger round? .50-cal rifles already exist; no need to invent a big bullet that turns into two smaller bullets.
(Unless you mean something that starts out the same size as the one in the video, in which case I can't imagine that two halves of a .30-06 would penetrate any better than one whole .30-06.)
There's often an advantage do a dual-mode strike. That's how many existing armour-piercing weapons operate. E.g., tungsten-alloy armor piercing rounds:
For anti-tank munitions two rounds work much better than a single larger round - the reactive armor is able to defend even against the larger round, but once it is hit once, it is gone from that spot until maintenance. E.g. the recent Ukraine conflict experience shows that many types of weapons can achieve successful penetration when (and only when) hitting essentially the same spot a second time.
And of course there are things like RPG-30 Kryuk to exploit that - fires two rounds, the first, triggering round is small and just enough to trigger the protective armor, and they're both fired at once from the same device to ensure that they hit the same spot just one of them tuned to hit juuuust a bit before the main round.