Well... the thing about the free radicals is that, they are in the oxygen. The only way Gaspar is not releasing free radicals into his body, is that:
A) He's not breathing, but there's a good piece of evidence that shows he breathes(remember the sleeping)
B) There's no oxygen in the End of Time, and somehow people can breathe without suffocation.
I know it's a game, and probably the dev team didn't thought this through, so chances are there is just not a clear answer. But aging is a by-product of breathing O2, completely outside of time. If you breathe, you age. According to the free radical theory, of course.
And don't be so concerned about breathing your life out, rather, enjoy it to the fullest!
As I said earlier, I think there's a lot of beauty in that idea, that which gives life, takes it away at the same time.
It shows that we are all running in the circle of life, because "life" doesn't have antonym. Death is the opposite of Birth, not of living. I believe just an ecosystem, the universe is a big cell and has it's own cyclic process, think about it, the earth has it's own process for healing itself. Just like the cells and the more complex organisms. Thus life is a wheel, we born, we live and then we die, by the same hand. It teaches us about balance.
Even proteins are harmful to the human body in extreme amounts, life is all about balance. Remember that life must be bittersweet, you can appreciate your moments of happiness because you know of sadness. Thus, life is beautiful, only
because it ends.
But... I have rambled too much again. Suffice to say that, even though Gaspar in theory should age, perhaps he doesn't, for whatever reasons the devs thought, and frankly, because I don't think they really thought that much of it. We, as fans, are in charge of dissecting everything in the things we love, not the creators themselves.
Just my thoughts on the matter, of course.