I think it makes sense that there would be slightly different rules for punctuation in memes than for punctuation in normal circumstances.
One of the functions of punctuation is to supply clarifications in written format for what would be conveyed in the spoken format by other means (pauses, tone, face/hand expressions etc.) So, if the meme supplies that clarification via other means, the punctuation could be seen as redundant. For example, I don't think you need a period at the end of memes, or a comma at the end of the top caption (I think the space between the captions is sufficient to represent the pause the comma stands for).
But it's probably a matter of personal preference (as long as people are mostly consistent within each meme, and the punctuation isn't distracting).
Caption this Meme
