Well, R. Lee Ermey's videos are for enterntainment first, and historical accuracy second. He's already decided in advance what weapon is supposed to win, and the videos are then rigged to make that happen.
Every single test was done in favour of the katana (and it seemed like the ice block had a bigger groove than during the longsword-test).
They cut against the soft leather (that no one would wear as armour anyway, unless combined with other armour, since the leather wasn't thick, multi-layered, studded, or hardened) where the longsword would be used to thrust, or use a point-slash (i.e. towards the tip of the sword).
And thrusting *through* the steel is an obvious win for the katana since the sword is more rigid and won't bend/flex at impact like the longsword will. Not to mention the longer blade on the longsword makes it harder to make a thrust against solid armour stable.
The longsword would be used to thrust at the throat, armpits, and other unarmoured or weakly protected spots, since trying to get through plate is only done with a warpick/pickaxe, and other armour piercing weapons.
Summed up, it's a silly test that proves nothing at all, other than that the katana is good at cutting styrofoam.