What kind of non-computer based hobbies do people here like to do, especially ones that stimulate the same hacker mindset as programming?
Both crafts are heavily focused on making jigs and precision. Then as you become better you find ways to improve your speed.
Wood working is a huge craft much like programming. Go watch some videos on https://www.reddit.com/r/woodworkingvideos but be weary its easy to get lost for hours.
If you have money and space think about a table saw and build some jigs for it(its like getting your IDE setup).
If space and moeny are a problem look in to joinery to get started. Hand cutting "dove tails" is extraordinarily gratifying and can be done with minimal investment while you are learning but as you will see the price quickly gose up if you want the best tools.
If you have more specific questions about wood working or welding let me know (PM's are best) I could talk for days.
Any sport, but particularly tennis, has a lot of challenge in terms of getting better. Lots of people like pickup soccer on a small field or basketball.
If you are involved with kids, coaching them at sports can be fun and challenging.
I also have some interest in improvisational acting and running pencil and paper rpgs with more of a focus of playing characters than simulations.