Surely most business sims fall into this? Capitalism, or Railroad Tycoon for example.

For some reason, it might seem that there are more non-war strategy titles that are in real time and less that are turn based?

nope

This is the Police. Definitely yes.
Papers please no. Offworld Trading Company has a frantic pace. A game were either you need to play decisively and even aggressively. You use the success of your adversaries to step over them. A bit like you can do sometimes in Imperialism, to mention a very different game that also boasts cutthroat economy.
Did you try Invisible, Inc.?
Good tabletop games, hopefully the conversions are nice.

Hey, good idea, thanks for the tips, made me want to look up some of these!

The Guild 1 and 2 are games where you control a business in a city, engaging in the politics of the city and trying to buy more business. You have a main character that can marry and have heirs, but also control the workers of your buildings, there's combat too, if you choose to manage a guardhouse business or be a thug, but it's just one of the many jobs available.

There's also city builders like Emperor Rise of the Middle Kingdom, Caesar, Zeus, Pharaoh where there's combat, but the blunt of the gameplay is mostly managing your city.

There's King of Dragon Pass, also has combat, but you can play a pacifist tribe entirely and just manage your tribe alongside the other clans. And the game is kind of Choose your own ADventure with choices and stuff.

Theme Hospital is a game where you manage a hospital and Prison Architect one where you manage a prison.

Hmm, the term strategy does assiciate directly with war, but otherwise it would be tied to resource management games or economic simulators. Usually this is a means to an end, like in Settlers where a strong economy produces a better fighting force than your enemies.

Unfortunately, there are plenty of games that could otherwise be listed here, but there is a small aspect of their gameplay that disqualifies them from this. The Patrician and Port Royale series come to mind.

Airline Tycoon might be a better example, where deploying your airplanes efficiently has some strategy involved.

Simcity could also count as one, how to grow your city needs plenty of planing.

By that broad definition almost all RPGs, board and card games would be part of the strategy genre, too, though. Maybe even sports games.

Let me revise my wording: The PRIMARY mechanic of Card City Nights is a strategy game (displayed as cards). There's little "game" outside of that.

Stronghold has, separate from the military campaign, economic scenarios whose goals are to develop a local economy, the only combat being the occasional scuffle with bandits.

Does PC Building Simulator count? I haven't played it but I intend to.

Really? As I remember it, you had to find a weakness in the opponents deck, and adjust your deck accordingly.

But sure, it is pretty casual!

Aven colony!

Is very much focused on colony development, almost no military/combat.

The closes you get to military are the 1 or 2 scouting ships you need for the campaign, or just for fun (you cannot actually drive them, only direct them)
The only other military thing are automatic gun turrets, but again, you only have to have those in the campaign, sandbox you can do it without them because they give you alternatives that work just fine, so you can play this game completely not military if you want, not a single weapon of any kind in sight.

The only enemy that attacks you in sandbox is viruses and fungus - most would say these enemies are exceedingly dull, but it sounds like this is what you want! lol