"The International Energy Agency defines it as "energy derived from natural processes that are replenished at a faster rate than they are consumed"
You want to use another definition, that's fine by me. I'll stick to the generally accepted ones.
The OP didn't know the difference, now he does. I think that's a good thing, no? If I used incorrect terminology to describe something, I would prefer it if this was pointed out to me. It makes it easier to communicate.
By the provided definition, solar and wind are non-renewable. They are just sun/fusion energy collectors, and the sun is not regenerating its fuel...
...it just has A LOT of it. Sort of like another fuel available to use, called Uranium and Thorium, and every other fissionable radioactive element in the entire universe.
By the time we run out of nuclear fuel, we will be making gravity-confined fusion reactors with shells made of solar panels, aka artificial suns for energy.