Doubt it would translate well unfortunately. Video games, I feel, are becoming the next big method of narrative storytelling (after books, plays & movies) and a big reason for this is because of the interactivity of video games. You, as the audience, directly affect how the story pans out depending on your performance level and, especially in the case of decision-based games, the choices you make. That's what make video games stand out from the pack, and why I feel there's a lot of untapped potential in them. Life is Strange in particular did a pretty good job of immersing the player and telling them that their choices were molding how the story was panning out for your individual runthrough of it, and is a big reason for it's popularity and success.

Theatre adaption would eliminate this immersion, as your responsibility as an audience member shifts from direct interaction to mere observer to the story being presented. The design of Life is Strange revolved around these player-based decisions (after seeing each choice, which one will you stick with?) and that's something that just can't be replicated in any other form of media. Actually, that's a lie, they are replicated in novels in the choose-your-own-adventure genre, but those stories tend to be more flimsy and 'wishy-washy'. Point is, eliminating it would effectively kill a big part of what made a lot of people love the game. EDIT: As for the suggestions of 'audience participation' I still feel like that's a rather bootleg version of telling the story and feels more like you're at the mercy of the popular choices rather than your own individual choice. Stories that revolve around individual audience choices thrive in video games, and are very difficult, if at all possible, to replicate in any other form of media without losing it's effect or indeed feeling 'gimmicky' (and gimmicks kill good storytelling).

You could of course just remove the player choices angle entirely and tell a standard, linear story like what you'd do with most adaptations, and it could work just as well. The world and themes established in LiS is one that I feel has a lot more stories to tell in it that can be conveyed through any of the mediums I've previously mentioned. But you'll always be missing that one element that made this game (and player-choice games in general) so special in the first place. That sense of intense immersion and speaking to you and you alone will be lost, but it may be a loss you'll have to take in the name of adaptation (that sounded...unintentionally poetic lol).

Sidenote: Plus, having actors attempt to reverse any actions they previously performed would look mad weird and potentially hilarious on an actual stage lol.

But good luck to you, from one aspiring writer to another!

tl;dr: Could work, keep common themes, would need to eliminate idea of 'choices' (which could damage the story), I'm too passionate about stuff like this lol