What validates the definition on this web site as correct?

The additional etymological information and the references are used to validate the definition provided.

How is "atheism" not an "ism?"

The "-ism" suffix belongs to "theism" (which includes belief in one or more deities).  The "a-" prefix in "atheism" essentially indicates "absence" [of theism].

Is atheism a form of dogma similar to theism?

No, atheism is not dogmatic.  Theism usally has a dogmatic basis that originates from religious faith in the existence of one or more dogmatic deities.  The "the-" prefix in "theism" means "from deity" and the "-ism" suffix means "doctrine."

The "a-" prefix in "atheism," which means "without," indicates the "absence" of "theism."  (Please also note that anti-theism is the diametrically opposed viewpoint of theism since the "anti-" prefix indicates opposition.)

Why aren't you worried about being punished in the afterlife for your blasphemy?

This is not blasphemy, and many atheists tend to be absent of belief in theistic concepts such as a deity-dependent afterlife.

Doesn't the definition on this web site describe agnosticism?

No, agnosticism differs significantly -- while atheism is the classification of "absence of belief in deities," agnosticism is the classification of "absence of knowledge about deities."  (Please also note that this differs from "Huxley Agnosticism" which asserts that there isn't sufficient evidence to prove or disprove the existence of deities.)

See also

For additional answers to questions about atheism:  https://www.atheistfrontier.com/faq/