Okay, okay.
I mean for the most part (except the horse thing which I'll explain) it's a great overview of Caligua, and a minute really isn't enough time to go into detail. So a TLDR: Good short, here's some more detail.
Much like the short said, Caligula's nickname came from his wearing of a soldiers uniform while young, but he absolutely hated the nickname as he grew older.
His reign's start was so popular in part due to the emperor who came before him, Tiberius. In Tiberius' later life he became incredibly paranoid of revolt or assassins so retreated to the isle of capri and started implementing secret courts and other more authoritarian measures as a means to control the citizens. Some of Caligula's family were victims of this. He dismantled these courts and even surprisingly got along well with the roman senate at first, earning the love and admiration of Rome.
Caligula's fall to madness was hinted at in the short and happened when Caligua got dangerously ill to the point his life was in danger. Romans prayed to the gods making offerings to the emperor's health, but the senate grew worried. They didn't want Rome to fall into anarchy should Caligua die, so started work trying to find a potential successor as he had no children of his own. Caligua saw this as the senate trying to replace him as emperor while he was in a weakened state, and once he recovered his relationship with them was a lot more cautious and icy. He had the potential successor killed so they could not hypothetically replace him and grew more paranoid of others in the city or senate who could try take his place, becoming a lot crueler and ruling through fear to enforce obedience, much like Tiberius before him before his Praetorian Guard (the emperor's personal bodyguard) assassinated him.
Oh and because I said I'd explain it, the horse thing was a jab he made at the senate for their slow decisions, a joke he made at their expense saying "My horse could be a better senator than most of you" and while he may have followed through with the joke, he was assassinated first. So while a funny image, no, he never made his horse a priest, politician or anything similar.
@mylesdenton1819