[edit: also, by thinking, I generally mean problem solving]
Somewhat open world games like Fortresscraft: Evolved - build machines to accomplish x goal. The thinking is a matter mostly of logistics.
Heavily modded minecraft has the same feel - find resources, mine them en-mass, turn them into things that let you get other resources, on and on until you make the last thing. If you're familiar with MC mods, reactorcraft is about as complicated as things get on that front.
Factorio, again, is mostly logistics puzzles. Some logic-gate thinkineering thrown in there.
The Forest is a survival/horror game is another that requires some thinking through.
Civilization franchise and similar turn-based strategy game - plenty of thinking to do there. Goal is to beat all the other opponents.
RTS is similar to its turn-based counterpart, just faster paced, but typically less in-depth for that.
I don't spend much time, if any, playing PvP games except from time to time when madness and I play SC2 on 2v2. Though that's mostly a matter of memorizing build orders and keeping track of as many tasks as you can at once. Not so much problem solving, but still fun.
Even some RPGs which have some broader elements of choice can do the trick for me, though I haven't found one I really enjoyed in a while. I tend to play them as close to stealth games as I can. Finding a clever way to circumvent a challenge rather than just powerleveling until mashing attacked over and over is successful.
Even some online CCG games I can waste a few hours enjoying. And that's not to say I don't enjoy idle games here and there, but I generally like to play my games, rather than watch them be played for me - I don't watch Let's Play videos for that reason. I like some moderate problems to solve.
I'm not talking about figuring out Millennium Prize Problems for fun in my free time. Hell, there are plenty of online college level courses you can find if you're interested in learning something. I'm not. You'll also notice I didn't put down games such as Kerbal, which I believe is way beyond the amount of thinking/problem solving that I want to do for fun.
What exactly is a strategy game getting at?
Same thing every game is getting at, to win? I'm not sure I understand your question.