This is just to supplement Decency's answer (below) for readers who are unfamiliar with Brood War; please read it first https://gaming.stackexchange.com/a/74844/20893. I agree with him, you just can't do BW muta micro in SC2. But what exactly is it that you can't do?
Sometimes it's not clear what BW players mean by "mutalisk micro". I think it's easier to show in-action than to describe it in words, but I'll try both.
Along the veins of the Jaedong vs UpMagic video in the question, and the Jaedong vs Iris video in Decency's answer, I'll add in Jaedong vs Fantasy (it's actually not his best) and July vs Hwasing (how it all started).
The Liquipedia article on Mutalisk Harassment is a textbook resource explaining the mechanics and advantages of muta micro, but it doesn't hurt to repeat the points here.
Allows the mutalisks to be moved like 1 unit
Allows mutalisks to stack their damage on the same target
Prevents opponents from focus firing down single mutalisks. The targetting AI would generally pick a different mutalisk every time the mutas moved out and then back into range. Since the mutas were stacked on top of each other, an opponent had a hard time clicking and picking a specific mutalisk
Targetting & Moving
Mutalisks belonged to a group of units (Vultures, Wraiths) that did not need to decelerate while firing because they fired projectiles. They could fire on the move!
As long as the the target was < ~30° of the direction the mutas were facing, the projectile would fire. This meant that sometimes the mutas looked like they could shoot sideways or backwards.
Slight variations in how the game interpreted the Patrol, Hold Position and Attack-Target commands meant the mutas could concentrate all their fire on one target or spread out the damage amongst multiple targets to prevent overkilling one unit.
Here are some detailed discussions on how to pull it off.
At the risk of sensationalizing the results of mutalisk micro (because it's not quite this good), imagine fielding a 1320 HP (120 HP x 11 mutas) unit that dealt 99 dmg to the first target (no upgrades on either side), and then 33 dmg to the second target and 11 dmg to the third target. Then imagine that it didn't even need to pause to attack, could shoot sideways, could turn 180° instantaneously, and slowly regenerated health. O_o!?
In the case of Jaedong, because he could micro 2 control groups of mutalisks (it's mind boggling to think about the mechanics of it), his Mutabehemoth was a 2640 HP, 198 dmg (then 66, then 22) natural disaster, rampaging across the map.
You'll notice in the Jaedong vs any-other-player games, the commentators' camera almost never leave the mutas. That's where the game is - the whole game. Jaedong's mutalisk micro controlled the game.
Now imagine taking that away from him.
The Pain of Switching Over to SC2
In the case of Jaedong, his virtuoso mechanics depended on the idiosyncrasies of BW. I really appreciate that Decency explains the latency reason for why it can't be done.
Even for the average competitive player, the exploits in BW made the game distinctive. For the more dedicated Zerg player, deep understandings of topics such as "Which Way Does the Mutalisk Glave Wurm Attack?" meant that SC2 feels like a completely different game.