Religion

They just defined the word as it made sense to theists which is in terms of belief as if someone has to make a decision one way or another.

Gil isn't the only religionist I've seen insist on a definition which requires belief, even though this is the least literate. Naturally this makes the most sense to them as they can frame both sides as requiring belief and therefore equally valid. The best part is both sides aren't equally valid regardless. Theism makes extraordinary claims. Atheism, regardless of their subliterate definition, does not. So no matter how you frame it, they are intellectually bankrupt.

The Collins dictionary is published in England. The version Gil referenced is the abridged version for American US English. In other words, it's primary purpose is to serve as a reference for UK English speakers parsing US English. If you go to their version for their native version of English, you'll find atheism defined nearly exactly the same way virtually all US dictionary publishers define it, which is a bit ironic. At any rate, if your objective is to be something less than fully literate here in the US, using an abridged dictionary published in the UK for American English syntax is a great start.