i was just discussing with a friend a few days ago about how the doge meme basically forces one to write a very short précis about an arbitrary topic, as opposed to lolcats which are themselves the object of the joke, or at most function as a metaphorical symbol.
i guess you can think of doge either as a sort of haiku, or a degenerate cinquain. my suspicion is that the popularity comes from being a hack which allows anal-retentive amateur grammarians to sidestep their ridiculous inner censor for a few seconds and just communicate their feelings and surface-level impressions. that’s why it’s a faux-pas, as mentioned in the article, to use nearly-correct grammar in a doge; it infringes on the purpose.