So I know the general ideas behind why to rest cut meats, but was wondering if the same applied to grounded meats (particularly burgers). It seems that biting into a burger is more tearing pieces off of the whole rather than cutting individual cuts, so the juices won't flow out...right?

You should let burgers rest aswell, yes.

try resting in the pan also if you're panfrying. works wonders with a fresh bay leaf