I remember trying out a zombie running app ~15yrs ago and am a fan of the concept. That was a podcast pretty much, audio-only storyline in your ears describing proximity/urgency/etc. I didn't grant this thing GPS access (work computer), but my immediate goal was to figure out how much attention it wants while running. The real problem nowadays (running in a city on city paths) feels like I would be oblivious to the people/cars around me and end up a safety hazard.

Yes, that can be a real safety problem. When I use it while running I only look at the screen when it warns me by vibrating. Vibration means zombies are nearby.

Sometimes I also use it while walking, in this case I feel safe looking at the screen even in the center of Lisbon which is a very busy city.

You're probably thinking of Zombies, Run!, which was an incredibly popular game that went viral over a decade ago. IIRC it did use GPS, but more for tracking your speed, distance, and overall movement. I don’t think it used your precise location to determine the proximity of zombies, though. Was a pretty fun game.

https://en.wikipedia.org/wiki/Zombies,_Run!

A zombie game properly paired a decent pair of "AR glasses" (that worked well outdoors) would be great fun to just head over to the nearest unoccupied soccer field and run for hours tho.

The game controls are not clearly visible. I am confused & figuring it out by random key-mouse combinations.

There are no mouse or key controls. You control your player by walking or running in the real world. :-)