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In the BRB, under the rules for assault, it reads: "a unit that fired in the shooting phase can only charge the unit that it targeted during that turn's Shooting phase."

Does this still apply if the unit is destroyed in the shooting phase? Like, if the unit no longer exists, clearly I can't charge it. But does it still prevent me from charging another unit, even though it is no longer there?

short answer:

still applies

Unless the destroyed unit was a transport, then you can charge the meaty goodness that was inside.