Those are tendons in fingers that respond to hypertrophy for climbing, or more specifically the tendon collagen, not muscles. But that's only one strength component of climbing, probably more so for bouldering specifically, but hand grip endurance and power also require forearm strength as well. I am not sure if that would be helpful for sitting in front of a computer.
I returned to climbing after a long hiatus, and my issues with discomfort and kinks in my back while sitting for long periods sorted themselves out in a couple weeks.
