I think about it in the following way; lifting weights is good for your body and strength but muscles grow during the recovery phase. If you don't add in recovery days, your muscles will not be happy and injury is right around the corner. From a narrow point of view of lifting/exercising, recovery is a waste of time since you can only gain if you lift. But if you don't consider recovery as part of the training itself then you're not going to last long until your body forces you to slow down.
Now consider the brain and the mind that doesn't shutdown even when you go to sleep and are supposedly physically resting. Applying the same process used for muscles is necessary. The term used if you don't do that isn't "mind injury" though, it is burn out and corresponding mental health issues("brain injury" is reserved to mean something else).
You need a way to "rest", whatever that means for you. If it's a game of Civ, then great. Reading a good book, extra great. Unfortunately while TV used to be a source of entertainment, I don't believe it is serving that purpose anymore. Why give up Civ if you enjoy it? Limit the time if you think you have better things you'd like to do.
For me, I've incorporated rest and downtime into my life after experiencing what happens when you don't. Having said that, it is still a battle some days if I'm not mindful because we're so used to being "productive" every waking second and actively discourage resting.
I also strongly encourage you try some meditation. It is very simple to do but not easy.