Thanks for the your explanation, Dave. I mostly agree with your interpretations. I understand what was attempted, but for me it just doesn't work.
I think your best point is about how the shared laugh bridges the shared mental instability of both characters.
I didn't interpret the story as manifesting the complete meaninglesness of their lives. I think within the story, their actions are significant. I interpret the raindrops hitting the ground and fading away into the puddles as life going on in spite of the significance of what occurred with them. And as you said, the merging of the two also manifests their shared experience and instability.
Your interpretation might be closer to Moore's intent, as it would parallel Moore's scripted nihilistic views of Rorschach in "The Abyss Gazes Also" chapter of WATCHMEN.
