I think this depends a lot on the team you’ve got. If you don’t have a technical co-founder or CTO type that’s in charge of overseeing the technical side of your business, then you’ll be well served to familiarize yourself with some of this stuff. Having insight into the technical side of things can help you to better understand the state of your business. You’ll also gain an understanding and appreciation for what your tech guys are dealing with, which can use to better manage them.

Keeping an eye on your code repository (reading commit messages) is a worthwhile exercise. Some of it might be over your head if you aren’t a developer, but perusing a bit will help you understand the state of your application. You shouldn’t need to learn git to do this - GitHub or whichever service you’re using will have a web-based interface for you to browse.

Echoing what others have said, business analytics is a big one. Understanding how to make the most of things like Google Analytics, MixPanel, etc can be very worthwhile. Integrating these into your application is a job that will fall on your developers, but deciding what to track and interpreting the results is something you can/should handle.

Should you learn vi or go digging through logs? It’s probably not the best use of your time, but if you’re truly curious then I say go for it.