You say what the user aboves avatar is thinking... Doesnt get any more basic than that.
Here's an example: I'll use my avatar.
User below: The user aboves avatar is thinking about noodles.
(I don't think there is a game for this already)
So let's started! Just do your best not to mess up.

^That Avatar^ Is thinking, "How do I hold these Chopsticks?!"

^that avatar^ is thinking. "peanut, if you wake me up again, I'll hit you."

Why am I in such a small circle!

^this avatar is thinking "why do I keep changing?"

users avatar is thinking "I'M A WRITER, WHY CAN'T I MAINTAIN THE PROPER RHYTHM FOR A LIMERICK!!!"

That's what I myself was thinking as well - Sometimes I write good poetry.

User's avatar is laughing at my pathetic limerick.

The users avatar is think "OHHH THE HORROR!!!!!!! I'M GOING TO DIE!!!!!! I'M GOING TO DIE!!!!! I CAN'T WATCH!!!"

User's avatar appears to be thinking 'WTF?'

Users avatar is thinking "Just leave me alone!"

User's avatar is thinking "Ow - This bowl is really hot. Why did I rest it directly on myself without even a plate?"

He's thinking "NOOO!" but about what?

he's thinking "**** Naruto got me addicted to ramen."

... Something about a riddle. I can't make out his thoughts completely.

The user's avatar is thinking: "Hmmm ramen.. hey someone is looking at me"

He's thinking "what nonsense is this?"

The user's avatar is thinking 'Derp.'

It looks kinda silly when you zoom the image up to full size. (Yay that one chrome extension that lets me zoom images by hovering my mouse over them.)

Huh... I'll say "OH MY GOD! WHAT PART OF LEAVE ME ALONE DONT YOU UNDERSTAND!"

"I'll eat your innards!"

"Oops I did it again."

"I wish I could set this ellipsis to move horizontally rather than vertically, it's rather hard to read this way."

Oh and I have a randomizer just because I want to be difficult
So it's gonna be one of these images here so yeah

"I'll keep changing myself, just to be mean!"

"I-I think my face is frozen!"

So many people think i think about noodles... how ridiculous...

I'll just take a nap right here.

“Yes, Mr. FowlJ, soon you will not be able to escape! With my exquisite beard-powered weapon of mass destruction, not even you can survive! I can see you covering your eyes already!”

^"paper = you lose!"

“It’s almost as if… my right eye pops out of my face somehow!”

(We can mildly diss the avatars, right?)

"Lol I'm a die, I can't think."

^ "Aye, 'tis a peculiar problem ye comes with"

"Lolwut?"

"derp"