I started indoor climbing 3 months ago and it's done wonders for my grip strength, as well as my overall health. I can't recommend it enough for engineers and other problem solving addicts. I was, frankly, bored by weight training and other more traditional exercise routes. Now I look forward to a nice change of pace - solving physical problems as opposed to logic problems.
I second your recommendation. For various reasons I haven't been doing it the last few years, but it was really good for me and I'd like to get back into it.
Another non-team sport that has good problem solving aspects but on a faster pace is trail running. You don't get the same thinking through a route you might have with rock climbing, but leaping over rocks and ruts requires some quick subconscious analysis and careful pacing that can be quite exhilarating.
That sounds like it is very high engagement and requires presence. I get something similar riding a bike in traffic, which is logically stupid but experientially great.
