I think Musk is referring to a quote made famous by Robert Oppenheimer. Upon witnessing the detonation of the first atomic bomb, Oppenheimer recalled a line from the Hindu sacred text "Bhagavad-Gita."
Now I am become Death, the destroyer of worlds.
I won't pretend to know Hindu scripture, so I'll leave any explanation of the religious side to people better trained than I. For Oppenheimer, the line is often taken to mean his horror when witnessing what he helped create. When I was researching this answer, I saw it might also be an attempt to say, "it was my duty to create this, no matter how terrible it might be."
For Musk's adaptation, he made two changes. First, he said, "I am become meme". As other comments noted, this is archaic usage with a misuse of count nouns. A correct usage would be, "I have become a meme." English speakers would forgive this usage for two reasons. First, Musk is trying to parallel an existing quote, and minor errors are generally acceptable in order to match the original. Second, the original quote comes from a religious text, and religious texts often use archaic language. Even modern translations will deliberately choose archaic language.
I don't know what he means by "meme", but I'll guess. Memes generally refer to pictures with humorous or ironic text written over them. More generally, memes can also mean expressions that appear repeatedly. Perhaps Musk means that he is no longer an entrepreneur or an inventor, but has now been reduced to that guy who "destroys shorts."
The second change he made was to say he is the "destroyer of shorts." Musk has gotten in trouble for his attempts to disrupt short sellers, investors to engage in high-risk deals that gamble that a given stock will lose value. He is especially critical of short sellers that gamble that his companies will lose value.
If you combine these changes with the holy scripture from which he started, you get a quote that implies that Musk has some sort of holy mandate to ruin investors that bet against his companies. I find it a bit disingenuous to equate a holy text and one of the deadliest weapons known to man to a pissing match between an entrepreneur and a few stock brokers.
If you wish to read more about the history of the original quote, here is my source: Oppenheimer quotes: the story behind 'Now I am become Death, the destroyer of worlds' | WIRED UK