Force quit closed application
From searching online, I think I may have run into an edge case. My best guess is that, having just installed Mojave, one of the many new permissions dialogs was generated but hidden behind another window. As I closed programs, some permissions dialogs appeared, including for Chrome. This doesn’t make much sense as a cause but it was related to a major system change so it’s my best guess.

I wound up resolving the issue by rebooting.

Edit: I had the problem again a few more times. Today, FlowVPN wouldn't force quit. I had to hard reboot because macOS was waiting for FlowVPN to close and it wouldn't.