Randy was an emotionally stunted, unmotivated, attention seeking loser.
Increasingly withdrawn, obsessed with his fantasy world, and too much of a pussy to do anything with his life, Randy decided to make is mark in the most cowardly, easiest way possible- by killing three innocent people and himself.
Thinking this would make him famous, he painstakingly documented his thoughts and emotions leading up to his finale, in an odd parallel to his EGS "Ghost Tapes" cartoons.
He worshipped the Columbine killers, and after realizing that no one would mention him in the news if he only took his own life, he flipped a coin to decide if he would take others down with him.
Some people say he was schizophrenic, but I don't see that in his videos at all. He may have been depressed, and maybe even a bit delusional, but I would argue that his delusions stemmed from the fact that he spent so much of his time immersed in his EGS fantasy-which was spurred on by the attention he finally received for his edgy cartoons.
In the end, he was poor (though thoroughly self documented) copycat spree killer, gaining minor notoriety due to the immature nature of his quirky obsession with becoming a cartoon ghost girl in the afterlife.