Show, don't tell

You need to convince your players that this situation could absolutely turn lethal if they don't play their cards right. As you say, it wouldn't make sense for the NPCs to outright tell them. (Though a snide remark of "I can't wait to see your skull break on the rocks" from a random NPC could work.) I think a better approach is to show them how lethal this could be.

Some suggestions

Find a reason to lead the players past the base of the cliff. Point out how high it is and how unnervingly fresh the bloodstains on the sharp rocks look.

Have the PCs overhear a conversation. "Did you see his face as he begged for his life? Shame that cliff isn't higher, then we'd hear them scream for longer."

Have skulls, lots of skulls. Put them on posts. Classic warning sign.

Execute an NPC. This is potentially the most direct and easiest. Simply have the NPCs execute another NPCs in a way that the PCs are aware of it. Death is on the table now.

More subtle

Have an NPC that isn't ok with murder. Mention their reaction (worry/fear/disgust/disappointment) when the player draws the wrong card. If the PC chooses to engage with them they mouth "RUN!!"

Alternatively have an NPC that's a huge fan of murder. Mention their reaction (excitement/glee/bloodlust) when the player draws the right card. If the PC chooses to engage have them draw a finger across their throat and grin.

Chance and Character Death

I think Linksassin has a great answer with regard to how to narrate the risk and encounter, but I do believe it is worth addressing whether or not your players are on board with an encounter like this.

Even with enough subtle clues, creating a path to fast character death that is out of combat may create problems at the table.

If your players are fully on board with this type of encounter and are okay with it, then there is no problem. But unless you know for certain that such is the case, you run the risk of creating some very unfun drama at the table.

Even if this is the final session of a campaign and the thematic ending of "life and death is random", that could still be a huge let down to the players. Remember that they have been heavily invested in their characters and developing an encounter that is entirely based on chance where the players don't even know the rules is roughly the equivalent of Rocks Fall, Everyone Dies.

Again, if you know that your players are on board with this, or they know that character death is something that happens regularly at your table, then this is less of an issue. But removing any player agency from character death is a big enough concern that I wanted to address it for you and for others considering encounters like this. We all know that characters can die, and often from poor decisions by the player, but making it happen due to random chance from a game with unknown rules may is a real concern.

As other answers have stated, showing them NPCs drawing a card and being pushed off the cliff or set free is a great visual to show how the card game works. I won't go into more detail on this as others have covered it fully. I do want to add...

Give them a long rest after pulling a card

Toss them in jail for the night. They might not need the HP, but this will allow the party to make a plan and allow the casters in the party to potentially swap out spells (depending on class) which might help them escape their fate. They don't even need to know what the card means, as long as they know that a card can mean either death or freedom. In my experience, PCs are very good at escaping executions if they are given a little time to prepare appropriately and make a plan.

A fairly simplistic answer-

Have them be clearly blood-thirsty. No language needed. Someone loses a finger? They go nuts. Someone gets freed? Disappointed looks. Back of the cards have a skull on them.

Then, when the fatal card is drawn? The crowd goes wild. Jumping and shouting and clearly very excited. If they're getting happy over a finger going missing, what on earth could get them so happy? Hang on, that's an awfully high cliff... and the cards all have a skull on the back.....

I think that's enough foreshadowing. Perhaps a smaller member could do an initial pre-preemptive "weak" shove if people still aren't getting it.

Let them see the outcomes beforehand

One way to let your players know what may befall them is to have them witness a the outcomes of a group of NPCs beforehand.

The day before their game of chance they are brought into a courtlike room and made to witness a group of NPCs go through the same trial they are about to face, however each card that the NPCs draw is predetermined to show off the various outcomes that are possible.

The question about taking away player agency can also be an issue. The solution I have used before is to create a plot hook out of it. Have a the remaining PCs meet a powerful Warlock or similar that knows where they can find/rescue their dead friend if they are willing to take a short jaunt through Hell. You could even talk to the deceased player beforehand and see if they would like to play as that character until their previous one is saved.

I find this method doesn't take away the fear of death for players but shows that there is a significant cost. If/when another player dies you can be sure the fiends and dark lords will be much better prepared if they attempt another rescue.

The classic way to do this is a riddle, prophecy or cryptic fortune telling

Such as when the witch tells Julius Caesar "Beware the ides of March!"
The message could come from a sphinx, a dragon, a hag, a cleric acting as a divine oracle, a jester, or any quirky fey creature... there are plenty of options.

Since they're going to potentially fall to their death, the cryptic saying could be something like "at a great height you'll soar" or seomthing that is variously interpretable.

Player agency is very important

What you're talking about here takes away player agency. They need it, no matter what. You're talking about one action that will result in an instant kill. And that's not fun for players. The whole reason why people play is to effect the outcome.

So, big obvious stuff--make it a ritualistic killing

Place artwork on the wall of the prison with people dressed up the way that their captors have dressed them, and maybe even makeup that's the same. (Maybe woad or something) Or have them find someone, rotting, dressed like this on a pile of bones at the bottom of the cliff. They must know something to make the choice. Otherwise, they don't know what the choice is at all.

Realism vs. Fun

At a certain point, realism has to take a backseat to fun. Maybe your players enjoy realism, but keep in mind that they have engaged in a game where mages, lovable rogues, and fantastic creatures roam. Do you studiously track every drop of water they drink and where they got it from? Do you occasionally give them dysentery without any warning? Because water can look clear, but it doesn't mean that it's not a vector of disease.