He took advantage of an uncharacteristic lack of planning by Saladin.

It's hard to say exactly what happened or how the military units were divided and how they manoeuvered. As R.C. Smail noted, "the medieval records give no tactical information." That's not quite true, since Saladin wrote some letters that can be used to piece together his movements, but for the most part it's pretty accurate. Medieval sources usually don't understand tactics and strategies very well.

We're not even really sure where the battle took place. William of Tyre, who was the chancellor of the Kingdom of Jerusalem and may have actually been present for the battle, called the site "Mons Gisardi." The name has typically been rendered in French as Mont Gisard or Montgisard, but it's not clear where that really was. Bernard Hamilton suggests Tell Jazar, which makes sense based on the similar sounding name. The traditional interpretation was that it was Tell es-Safiya, but that was probably too far away. It was also the site of the crusader castle of Blanchegarde, which isn't otherwise mentioned in reports of the battle.

In any case, Saladin brought an army from Egypt into the Kingdom of Jerusalem in October 1177, and encountered very little resistance in the southern part of the kingdom. There was a fairly large crusader expedition from Europe in the kingdom at the time, led by Philip of Alsace, the count of Flanders. But Philip was preoccupied with the city of Harim and Hama in northern Syria, so his army wasn't available to defend against Saladin.

Baldwin brought the army of Jerusalem south to Ascalon, at the frontier with Saladin's territory in Egypt. Baldwin was only about 16 years old at the time, and he was already being affected by his leprosy, so the army may have been commanded by Raynald of Chatillon, who was acting as regent for the king. Baldwin apparently thought his army was too small to confront Saladin. On November 22 he marched out from Ascalon, but then retreated back into the city.

Saladin allowed his troops to disperse and plunder the countryside. They raided Ramla, Lydda, and Mirabel, among other places. He also didn't leave anyone behind to guard Ascalon, either to prevent Baldwin from marching out again, or even just to report back to him if Baldwin left. Bernard Hamilton calls this an "elementary lack of caution."

Baldwin did indeed leave Ascalon and brought the army to Gaza, where they were joined by the Knights Templar. On November 25 they tracked down Saladin at Montgisard, wherever that was (clearly somewhere near Ascalon). Saladin's army was still widely dispersed and pillaging the surrounding land, and he could only recall the ones who were still within earshot.

Saladin tried to arrange his troops around the nearby hill (the "mont" part of Montgisard), but before they could be fully deployed, Raynald of Chatillon charged the centre of Saladin's army. One of Saladin's great-nephews was killed and Saladin himself was forced to flee. This seems to be what the TikTok video is depicting although it probably wasn't an neatly organized as the video seems to imply! Saladin's troops were spread out over a large area, he was trying to organize them into three or four blocks around the hill, and Raynald surprised him with a charge.

From the medieval reports of the battle it actually sounds like this may have been what Saladin was expecting - a common tactic was to allow the crusaders to charge, then manoeuver the troops out of the way to almost let them pass through, but then surround and trap them. Another common tactic was to pretend to flee from a crusader charge, but then regroup and attack when the crusaders were exhausted from the chase. In this case Saladin probably wasn't planning a fake retreat (since the hill was in the way) but he could have been planning to surround and trap the charging crusaders. Unfortunately for him, Raynald charged unexpectedly, before Saladin had put all his remaining troops where he needed them.

The two C formations in the video seem to assume that Raynald and Baldwin commanded two parts of the army, and purposely trapped and destroyed the fleeting troops. I guess that's a plausible interpretation, but I'm not sure that's how it really happened. At least according to what was reported in medieval sources, Saladin's army simply lost their formation and the crusader army chased them, killed or captured as many of them as they could, and also captured a large amount of booty. The Muslim troops that had previously wandered off to plunder the land were also easily captured when they tried to return.

Saladin might have been able to regroup his forces and counterattack, but the next day the weather turned bad and it rained for over a week. The local Bedouins also attacked the stragglers from Saladin's army.

So it turned out to be a major victory for Baldwin (and Raynald). Saladin seems to have been somewhat embarrassed and tried to spin it as a victory, but no one really bought it. Baldwin had a monastery constructed on the battlefield, to commemorate the victory and as a bit of propaganda, to show that Saladin's claims of victory couldn't be true. Saladin felt he redeemed himself by destroying the crusader army and recapturing Jerusalem ten years later in 1187.

Sources:

Bernard Hamilton, The Leper King and His Heirs (Cambridge University Press, 2000)

R. C. Smail, Crusading Warfare, 1097-1193 (Cambridge University Press, 1956, 2nd ed., 1995)

M. C. Lyons and D. E. P. Jackson, Saladin: The Politics of the Holy War (Cambridge University Press, 1982)