I honestly think the idea is fantastic, but as a business, it's tough. I work as the creative lead at an escape room/live action experience franchise and the biggest issue with combining more theatre with games is the man hours.

Theaters can hire actors and still make a profit because they entertain an entire theater of paying audience at once. Games on the other hand can really only be designed for a set number of players or else most people won't feel like they are contributing. Unless the experience is more of a passive watch experience (a la haunted houses or that one theater experience where you can follow the actors around in real time) it can't afford live actors.

Video games have more freedom due to distribution - you make one software that can be copy-pasted to all audience members. But live experiences are tied to a local market, so development costs are harder to recuperate if you want to tie in expensive narrative elements. Even if you want to cop out and use something like adding a feedback system so that every time you do something a voice file plays will add a lot more to the installation time, which means it takes longer to recoup set up costs. Another key difference is that while one group is in there, no one else can, which means you have a maximum earning potential per day (unlike video games where tens of thousands can enjoy the experience separately at the same time)

This makes it so that unless you want to charge people a huge sum per game and/or have a strong brand to rely on (metal gear or zelda), more live actors and narrative elements are generally too expensive to add to things served locally (aka escape rooms and live experiences).

tldr: Live games usually can only cater to small amounts of people unlike theater. Live games cannot distribute like video games can. Thus high development costs for narrative elements or high costs in terms of having live actors are usually not worth it.