Chicago has finance, it just doesn't have Wall Street. If you want to trade options or commodities Chicago is arguably a better place to be. New York is undoubtedly the better place to be for stock trading.
As far as entertainment goes, it's no accident that a huge number of comedians get their start in Chicago.
Chicago has tons of anchor industries, the real problem is that they don't translate well to the unicorn strategy of most start-ups.