Much of his wealth is held in shares of his publicly traded companies. If investors lose faith in his ability to manage and grow one company it could (and seemingly has) affect the value of all companies he's involved with, directly decreasing his net worth. Making Twitter profitable would have gone a long way in demonstrating his ability to run a company, but he has done the opposite.

But technically no, I guess he doesn't need Twitter to turn a profit. He could just watch it all burn.