What is militant? From Latin "militans" = "being a soldier, fighting". Atheists who fight someone or something for not being atheist are called militant atheists. In modern usage, "fighting" includes propaganda aimed at weakening its target. Dawkins would certainly subscribe. The question of what exactly he is fighting has become part of the fight.

(Note that Urban Dictionary is a valuable but extremely unreliable source, being written by presumed slang speakers themselves.)

Criticism is distinguished from militance/fighting by being aimed at particular features, theoretically allowing for reforms and corrections. Luther's theses are an example.

Dogmatic is a completely different notion: basing one's teaching on foundations that one excludes from all questioning. Dogmatic persons act authoritarian against their followers, but need not necessarily fight the heathen.

Zeal can have any target, but neither militants nor dogmatists can exist without it.