The most interesting thing here for me is the use of redirected walking (https://en.wikipedia.org/wiki/Redirected_walking). I saw the video accompanying the paper but this would be the first game I've seen try to use it.
But I feel we may be overthinking it. I believe simply tracking leg movement and having the player jog on the spot is the solution.
Having simulated this myself by holding forward on the controller while jogging on the spot, I believe it's the way forward. If you have a headset, give it a try. I admit walking doesn't feel very natural, but jogging works well.
Of course, games don't have this option with most popular current hardware (but foot trackers and whole body trackers do exist).
It would be tricky to blend/differentiate movement and jogging, but I think it's doable.
I predict that future headsets will do inside-out tracking of your entire body, including the legs (they made need a flip out camera to be far enough out from the body to do this). They've already put out a software update for the Quest that does surprisingly good controller-free hand tracking.
There was also a comment on HN a few weeks ago (I'll try to find it) where someone implemented this system and said it worked well.
There's a great low tech solution - pair your mobile phone and leave it in your pocket. The accelerometer data is more than good enough to detect jogging.
There was an app for Steam VR that did this and I recall it worked quite well.
EDIT: here: http://pocketstrafe.com/
I used to do gymnastics and as part of that I trained doing long series of cartwheels along a marked line. I managed to get good at doing it without deviating from that line. I looked straight ahead and it went fast enough that everything was a blur. However, I still couldn't do it with my eyes closed.
Redirected walking means distorting the mapping when moving or rotating, to fit any game world into limited playing space. In research it's always applied in larger spaces, x5 times bigger than living rooms. If you distort moving or turning too much, users lose balance or become nauseous.
Here's a decent intro paper. 15 Years of Research on Redirected Walking in Immersive Virtual Environments https://illusioneering.cs.umn.edu/papers/nilsson-cga2018.pdf