I really doubt you'll retain as much as dedicated reading if you are listening to a podcast and playing a game. Unless it's a game where you don't need to think/read at all.

Regarding walking your dog: that's true. Walking around is a good way to retain information. That's explained on Moonwalking With Einstein

Why on earth would I listen to a podcast while playing a game? Though TBH I mostly don't much care for background audio when doing other things that involve any real thinking. Podcasts are mostly for driving, cleaning, etc.

I don't do much thinking when playing a FPS game