I feel like this too. However, I've found I can instantly get into non-verbal focus while playing chess. You might want to give it a shot. FWIW I'm not a particularly good, or experienced player either, just someone that enjoys it.
I’ve hadn’t realized it until you just said it, but I am the same way. I’ve played roughly 10-20 games a day for years! That said, I feel I am simply trading one mode of thought for another. I tend to be _even less_ present when playing chess than nearly any other activity.
verbal focus helps my chess. when I think things like "he's trying to mount an attack on my queen's side", verbalized as words, it helps me to understand what I'm seeing in a new way