Both “secularism” and “atheism” are simply the absence of any religious doctrine or belief system.
Secularism - secular spirit or tendency, esp. a system of political or social philosophy that rejects all forms of religious faith and worship.
Atheism - 1. the doctrine or belief that there is no God.
2. disbelief in the existence of a supreme being or beings.
In both cases, just as darkness is simply the absence of light, secularism and atheism are simply the absence of any religious belief.
Socialism is a form of governance, which is largely dependent upon (but not the same as) secular or atheistic beliefs.
Where are you getting your facts? The column stated it exactly right, in proper context.