Nearly every notably brilliant programmer out there has other pursuits. You need to diversify your interests for your health and to gain inspiration from outside sources. Locking yourself into a bubble of software only makes you miss out on the world.
Hitting the gym can actually be pretty complementary to writing software or doing other sorts of engineering in the best possible way. For example, many people are psychologically messed up due to some sort of mental "baggage" that basically shows up as a somatic fight-or-flight response, albeit generally in an in-set, chronicized form rather than a literal stress reaction. This can place a significant cap on both your executive function and your self-perceived mental acuity. Hitting the gym is an excellent, time- and cost-effective way to work that stress out of your body and mind!
You need to devote a "non-trival" amount of time becoming a well rounded person or everything else is going to suffer, including your ability to maintain relationships in the workplace and communicate. That's way more important than knowing all the arcane details of the Java virtual machine.
I don't see how you could be an intelligent, creative person and only be fixated on one thing your entire life. The smartest people I know have all sorts of creative outlets. I think I saw something that said a very large portion of Nobel prize winners are musicians, too.
Personally, I exercise because if I don't my mood suffers. It's a big problem, which I have found a solution to. Don't judge people.
What did you just call me?!
You might as well not trust anyone with a family or any kind of hobby outside of programming to write a decent program.