You could absolutely make it an RPG!

You just need to zero in on what the story is about, and why that's important to the characters.
For instance: maybe the story is about what the characters lose in order to keep up their hunt. Every character is asked four questions about things that they value. The answer to each of these questions is a trait. (This is gratuitously stolen from Hollowpoint.) Entering new hexes means that you push your luck (because Zombie Dice is game), and when the odds turn against you, you need to give up a trait or abandon the hunt. The further you push, the more game you bring back. But the further you push, the more you risk running into a disaster that forces you to retire from the hunt or lose a trait.
Here's a quick-and-dirty example, actually. (Wrote it in about an hour and a half)
Building a CharacterYou are a hunter from the village of Nels. You normally hunt game to provide for your family, but you are currently engaged on a hunt for far more valuable prey: the White Stag of Glimspider Forest. You and your fellow hunters will search the forest in pursuit of the Stag, risking life, limb, and everything you hold dear.
Answer all of these questions but one (you choose which one), and write the answers down on an index card. Write your hunter's name above it. None of the answers may involve another player's hunter nor your own hunter's life.
QuestionsWhat is the oldest friendship that you possess?
What is the heirloom you carry that has been passed down through the family line?
What is your prized weapon?
What is your greatest ambition?
Whom do you love the most?
The answers to these questions are your
traits. They are your only means of survival. When you lose all of your traits, you are vulnerable to death.
Finally, each hunter picks two of the following
attributes:
Fierce,
Cunning,
Wise.
Venturing Into the ForestPlay progresses through a series of Hunts. Once all hunters have either retired, lost the Stag's trail, or captured the Stag, the Hunts end and play proceeds to the Epilogue. If the hunters all fall victim to the Forest, then the game ends in defeat.
Falling Victim to the Forest: Any hunter who loses all of their traits is in grave peril. If the hunters are unable to expend enough Attributes to defeat a newly-drawn hazard, then all hunters who have no traits remaining are immediately lost to the forest (with no chance to turn back), dead--or worse. They have utterly failed in their Hunt.
The first player (the Hunt Leader) steps forward into the woods, journeying forth to the village. They draw a hex tile from the stack, and place it on the edge of the village. The tile lists 1-3 attributes (Fierce/Cunning/Wise) and explains what hazard the players encounter. (You should have a specific set of these tiles; like the Green/Yellow/Red dice in Zombie Dice, some of them are more dangerous than others.)
e.g., a tile might say "Jaguar Lair: Fierce, Fierce, Wise" or "Roc Labyrinth: Cunning, Wise". Each player describes how they enter the hazard, preparing to meet it. This is a period of free roleplay and planning. At the end of it, the players must decide who contributes their Attributes to overcome the obstacle. Each Attribute a character expends is able to cancel out a corresponding Attribute on the tile.
e.g., the Roc Labyrinth could be overcome if a Cunning/Wise character expends both of their Attribute, or if a Fierce/Cunning character and a Fierce/Wise character expend the appropriate Attributes.When an Attribute is expended, it may no longer be used in the current Hunt. Place an "X" next to it. If the players are unable (or unwilling) to expend Attributes, they may instead lose a trait to cancel an Attribute on the tile. (They must then tell everyone else how the strain or peril of the hunt destroys that trait, whether it be a spouse who abandons them while they're on the Hunt, because of their obsession...or a wild animal that destroys their precious family pendant.) While players are choosing who will expend Attributes, any of them may instead decide to leave the Hunt and turn home. They erase the marks from their Attributes, and may no longer be involved in the current Hunt. They tell everyone how their hunter gives up on the hunt and finds their way home.
When enough Attributes have been expended to overcome the obstacle, the players who expended those Attributes explain how their hunters used those Attributes to help everyone through. The tile has now been beaten, and no longer poses a threat on future Hunts. Put a Clue token on that tile, as players gain more information on the Stag's whereabouts.
The Hunt Leader draws a new tile, placing it adjacent to the one just defeated. Play proceeds as before, with the players still on the Hunt deciding whether they will expend Attributes, with the option of turning back instead. As before, when the tile is defeated, place a Clue token on it. If at any time all hunters turn back, remove all Clue tokens from the tiles and turn the current tile facedown in its current position.
After a Hunt ends, have a brief scene of roleplaying where the characters gather around the campfire at night, pledging to return to the forest to hunt the White Stag. Then, play proceeds as before, but with two differences. First: the player to the left of the Hunt Leader becomes the new Hunt Leader. Second: the first tile is not drawn by the Hunt Leader but rather is the facedown tile from the last Hunt.
If there are three times as many Clue tokens as players, then you have made enough progress to locate the White Stag. Draw two tiles; you must overcome them both simultaneously. The hunters describe how they track down the White Stag, and then everyone describes how they help to trap and kill the beast, triumphantly bringing it home. Proceed to the Epilogue.
If you run out of tiles (not sure how many tiles, that'd be a game design thing), the Stag has escaped, and your efforts are fruitless. The hunters return empty-handed to the village. Proceed to the Epilogue, but Glory is set to 3, irregardless of hunters' remaining traits.
If all of the hunters have fallen victim to the forest, the game has ended in defeat. The village mourns over its fallen warriors, and bewails the folly which led its strong hunters to chase after such a beast. They will surely have insufficient food in the winter.
The EpilogueWhatever circumstances brought the hunters to this end, it's time to figure out what happens to everyone. Tally up how many traits remain; this is the hunters' total Glory. Then, each hunter picks an ending and narrates it, according to the following rule: your total Glory limits how many hunters may choose a Good Ending.
0-1 Glory: None of the hunters
2-3 Glory: One hunter
4-6 Glory: Two hunters
7-9 Glory: Three hunters
10-12 Glory: Four hunters
13+ Glory: Five hunters
Hunters pick endings in order of how many traits remain, highest to lowest. If you lost all of your traits, you're probably in line for an awful ending. Each ending may only be picked once. When you pick your ending, explain the details of how it happens.
Good EndingsYou are lauded for your part in the Hunt, and become chief of the village not long after.
Your children are seen as great and mighty warriors because of your exploits, and they will be courted by well-to-do suitors in the coming years.
You learn from your experiences, and become the greatest hunter the village has seen, bringing back more game than anyone else.
You saw a great and powerful secret in the forest, one that will assure your good fortune.
The White Stag let its gaze fall upon you when it was killed; you are granted a single blessing for you or your descendants.
Bad EndingsYour family starves, because your obsession caused you to neglect their needs.
You have lost your mind in the Hunt, and must live in isolation, only coming out to hunt enough food to feed your family.
You are cursed for participating in the Hunt against the Stag, and evil fates will follow your family.
You have been crippled by the Hunt, and you're not long for this world.
You have nightmares, and the madness that only you saw in the Forest calls to you. One night, you run to the Forest and never return.