The game they're playing is this called Coup and you can find a description on boardgamegeek (would post a link if I could...)
It's one of my favourites and I thought it would fit the two perfectly hehe

Light couldn't believe his luck. L had actually suggested bringing in Mikami for some sort of card game to "test his intelligence" against his own. Light's pounding heart had been difficult to control, but he tried his best not to sound too eager to agree to something that silly.

Mikami will come to the HQ, he will see L's name with the death god's eyes and when the time is right, he will kill him. Ideally Light will write the name into the Death Note himself, but he wasn't sure if he was going to get that satisfaction. He couldn't believe that it would be that easy.

Unfortunately L had insisted that they play right the next day, since it would be Sunday and the place would be empty. This means Light hasn't been able to sneak any hidden messages to Mikami, but it shouldn't matter. All that Light needed to do after the game was to ask Mikami for L's name.

"Does everyone understand the rules?"

"Yeah, yeah. Let's just start."

They were playing "Coup", a social deduction game that was all about bluffing and lying. Light hasn't played the game before, but he should be excellent at it. All he's been doing the past years has been bluffing and lying. If anything, he forgot how to act like a normal person.

Everyone started with 2 cards that each had a role on them with different powers. No one knew which cards you had, so you could use any power you wanted and pretend to have that card. If someone caught you lying however, you would lose a card. Once you lost your cards, you were out of the game.

Mikami seemed utterly confused as to why he was here, but Light had made sure to tell him how important it was that he showed up.

"I'm stealing 2 coins from you, Ryuzaki," Light announced and moved them towards his money pile.

"Aha. So Light is saying that he has the Captain."

"I am, yes. What about it?"

"Hmm. It seems strangely convenient."

The two were having one of their staring contests, completely ignoring the third person in the room. Anyone watching them might've assumed this was some sort of sleepover, not a "test of intelligence that is important to the Kira case", as L put it.

"If you're so suspicious of me, why don't you challenge me then?" taunted Light.

L shoveled buttercream from the plate into his face, never breaking eye contact.

The way he licked the remaining substance from his lips was awfully suggestive and Light wondered why there wasn't a single napkin in this massive office.

L smirked and seemed very pleased with himself.

"That's what I will do. You don't possess the Captain, Light Yagami."

With a superior sneer Light revealed his card. It was the Captain.

"You lose a life, Ryuzaki."

Despite this, L didn't lose his composure and turned one of his cards over.

Because Light revealed his card, he had to shuffle the deck and draw a new one. He also only had one life left. He wondered if he should increase his chances of winning. He felt the Captain card with his pinky as he slid the cards across his hands. He knew where it was. He could just... draw it again.

"Now I will steal 2 coins from you, Light."

"Not going to happen. I'm blocking you. With my Captain."

L stopped his hand that was reaching for Light's money.

"Another Captain?" said L and looked at the draw pile that contained 9 cards. "That is statistically very improbable."

"What can I say, I'm a lucky guy."

Light assumed a self-assured position on the couch. He knew the game was over. And he won. Technically he won the moment Mikami laid eyes on L.

"I will have to call you out on this."

An elegant hand slammed dramatically on the table and revealed the returning Captain.

"I'm dead," L announced and chewed his thumb, clearly lost in thoughts.

"There you have it. I hope you're happy with the results of your 'test'," Light chuckled maliciously.

"I...," they heard a stammer from the side, that got them out of their competitive mindset. "I will have to coup you, Light."

This would mean that Light loses a life in exchange for Mikami paying 7 coins.

"What?! Don't do that!"

"B-But I have to! I have 10 coins. The rules state that I have to use them, and you're the only one left in the game."

Light flipped his remaining card through the air in a childish way.

"Whatever."

He beat L, that's all that matters.

Mikami was eager to escape the strange situation. "I will have to leave. I need to prepare for a case tomorrow."

"I'll see you tomorrow after work."

Light made sure to lock in an opportunity already for when he would get Mikami to tell him L's real name. He gave Mikami a peck on the lips and didn't have to put on a fake giddiness for once.

He felt elated. He's finally done it. Nothing could get in his way now. L's death was inevitable.

Light positioned himself next to L on the couch. His victory would be even sweeter, if he could look at L's unassuming face just a bit longer.

"You seem very happy, Light. Even though you just lost."

Watari wheeled in a fresh supply of cake. L's fingers started prodding one of them, he was deep in thought. A fork was right next to the plate, which usually would have irritated Light greatly, but not tonight.

"I didn't lose. I killed you."

L drew an elaborate pattern into the chocolate mousse.

"That's because," he paused to lick one of his fingers clean. "You cheated."

Light got caught off-guard and couldn't stop the laugh that escaped his lips. He moved closer to L and made sure to look down on him.

"Doesn't matter. I won against you."

One of L's chocolate covered fingers touched Light's corner of his mouth and all of the sudden he felt how quiet the room was.

"You won the game, but you failed my test."

"You're getting chocolate all over me..."

"It fits Kira's profile perfectly to cheat in a petty game of cards."

L cleaned off the mouse on the other man's lip with his tongue and Light could feel the control of the situation slip away from him.

"Ridiculous," he managed to bring out of him, a lot quieter than he intended. "It just shows that Mikami played smarter than you. That's what your test was for."

Their noses were almost touching.

"Was it?"

Light couldn't remember who started it, but they ended up as a messy bundle on the couch, not being able to let go of each other's lips.

Victory was close, so he might as well let his emotions unfold, just once. Now he understood why it had been important all along, that he kept mental and physical distance to his persecutor.

Being like this with L almost made Light not want to kill him anymore.