Not religious means they do not follow any faith. One CAN believe in a higher power, but not be religious. Though technically that puts them in with the Agnostics.
I believe he's referring to one of the dictionary definitions, namely:
2 : of, relating to, or devoted to religious beliefs or observances <joined a religious order>
where you are taking the term religious to mean
1 : relating to or manifesting faithful devotion to an acknowledged ultimate reality or deity <a religious person> <religious attitudes>
Of course one could say YOU Achilles are religious as well
3 a : scrupulously and conscientiously faithful b : fervent, zealous
"I would rather be exposed to the inconveniences attending too much liberty than to those attending too small a degree of it." Thomas Jefferson