Exercise is certainly part of what's needed to stay healthy as long as possible, but nutrition, sleep, stress, and genetics factor in as well.

I find it interesting that DNA is a relatively stable molecule; what seems to fail as we age is the system that controls DNA expression. And we need good nutrition, good sleep, low stress, and exercise to keep that as stable as possible

For anybody interested in this, I'd suggest David Sinclair's 'Lifespan' for an intro to discoveries around how this all interrelates.