I can see how this could be boring or confusing if you haven't played the game. Even if you have played the game, it can still be confusing.
For maximum enjoyment, you might want to read a FAQ on speedrunning FF3. The "6:30" walkthrough on
GameFAQs isn't too bad and introduces many of the concepts.
Here are a couple of simple things that might help those viewing the game:
When a playable character gets down to a very low number of hit points (10% or lower of max HP), and is commanded to "Fight", there is a small chance the character will perform a "desperation attack" instead of a normal attack. The desperation attack is about 25X the power of a normal attack. You will see this often in the game -- Erokky gets one character down to 10 HP or so (by having the other players attack that character, etc.), then manipulates luck to make that player perform a desperation move. Very cool, especially since you can often get through the whole game without seeing a single desperation attack, especially if you're like me and always heal characters that go below 25% max HP.
Relics have various effects on the characters, and those are used carefully by Erokky. If somebody in the party is wearing Sprint Shoes, the player moves about 2X as fast, so Erokky almost always has somebody in the party wearing them. Earrings increase the damage of magic attacks, and wearing more than one Earring increases the effect. The charm bangle decreases the frequency of random encounters somewhat. The Moogle charm (usable only by Mog) completely avoids random encounters.
There are several "Instant Death" spells in the game. Snare, Doom, and X-Zone come to mind. If one of these spells hits, the target instantly dies. As you might expect, many bosses and higher-level monsters are hard or impossible to hit with these spells. There is a glitch in the system, though. If a monster has the "invisible" status, magic attacks always hit. So a cheap way to kill a monster is to make it invisible, then cast an instant-death spell on it. You can cast "Vanish" on most enemies to make them invisible. You can also tell somebody to summon the Phantom esper, then Muddle that character, with the result that Phantom might make your enemies invisible instead of your allies.
The Vanish + (spell) combo is also used for attacks that aren't normal spells. Gau and Mog can be told to "Rage" and "Dance", which means they go into an uncontrollable state and start performing various attacks at "random" (of course, there's no such thing as "random", esp. for a TAS). Both of them have Rage/Dance moves that cast "Snare", which is instant-death if it connects. So you'll see some moves where Snare seems to come out of nowhere (it came from a Rage or Dance command). On tough enemies, you'll see a Vanish command given first to make sure the Snare connects.
Setzer has a nifty Slot Machine attack which is the most powerful attack in the game. If the slots come up 7-7-7, you get Joker Doom, which is instant death to all enemies (and it always hits). Of course, it is a gamble: if the slots come up 7-7-Bar, you get reverse Joker Doom, which is instant death to all allies. Of course, the slots are rigged, so you have to "be lucky" to get the 7-7-7 combo to come up. The random number generator that affects slots starts at 0 for every fight. If the random number generator is in the wrong state, it won't let you get 7-7-7. Different events in the fight change it by different amounts. One easy way to get the random number generator to a state that allows 7-7-7 to come up is to use an Echo Screen item. On some boss battles, it is completely impossible to get a 7-7-7. Fortunately, 7-7-Bar is always possible. If Setzer is muddled and gets a 7-7-Bar (death to all allies), there is a chance that he will accidentally reverse the attack to make it reverse-reverse Joker Doom.