What do you want the titles to say or represent?
Would changing words to more unique words achieve that goal better? A phrase is conveying meaning, people will read the meaning and maybe not care about the specific words.
The tavern game's description sounds like those Lemmings games. I probably would have tried a title like "The short way home". But on second thought, they are not going home, but back to camp. "Soldiers - An after drinking game".
With the you are being hunted, I would have expected a horror game, where the hunters are hunted by a rabid deer. Not a deer protagonist escape game. "Deerscape". Or simply, "Deer Hunted" as a reverse of the known "Deer Hunter".
The balloon game is a horror game. The twist will not come from that title itself. Only from reading the subtext. That's tricky. If you want to attract your target audience, but your title alone would attract the opposite. Balloon games are rather known for being about fun.
As titles, all of those titles work. The only one I would consider changing is the Deer game. Hunter games with deer in the title are long established and invoke expectations. The "," in the title reads like a "-", since it serves no obvious grammatical function, as we usually do not talk to deers. Deer - You are being hunted. But that does not imply a subject shift from the you not meaning the hunter. Imho it implies the Deer being the hunter. You clear this up with the subtext of course and you felt the need to clear that up. For the title, you could just shorten it. "Deer. Be Hunted." or "Deer - Being Hunted." (That could still be read either way, but short of spelling it out, like "Hunting Season - You are the Deer", that's always a possibility)