Perhaps it would be useful to more clearly define strategy

Let's definie it in marketing terms, a strategy is a game that is put on the shelf called "Strategies" by the shopkeepers and clients do not complain it was wrongly placed :) I think such real life definition is far more useful than any academic distinguishion.

BTW I found a few examples!

Detroit, Old Timer, Oil Baron.

Which, I'm quite sure, would be done as realtime if these were to be released nowadays...

But basically all non combat strategy games seem to be either business games or simulation games.

Interesting thing, isn't it?

How about combat strategy games that do not use a map to move units? Anyone stubled upon something like that?

(I have, but it's one I made so it does not really count :) http://silverlemur.com/minigames/wartimeindustry.php )

The other way around applies too, though - basically all turn-based computer games can be converted to board games. There are lots of board games where you move units on a map to kill other units, from Axis and Allies to Dominant Species and simpler things like Risk.

On the contrary, these are pretty rare (nowadays, in the past indeed all kind of hex based wargames were domanating boardgames). The trend in boardgames is for Agricola, Puerto Rico, Le Havre, Power Grid, definitly unlike Risk.

The interesting thing, computer games don't have these mechanics... The "evolution stopped" at chess and we still redo this board with units over and over again adding more units, cities on some grids, diplomacy, but in the core it's the same kind of game. No revolution of any kind here, for some, unknown to me, reason...

If "strategy" is "make most optimal use of your resources" then I guess I could point out some real world games I've played with my friends.

Such game needs to meet ALL conditions below:
- turn based
- strategy (in a very broad sense)
- you don't move units on some sort of map to kill other units

There's no killing involved in Adastra, by Bruno Faidutti, albeit there are units to move on a map. I think it's a remarkably balanced game.
The game is based on acquiring resource cards by moving units on planets to mine.
The strategy involves maximizing your score and not giving advantage to other players. There's also a nice "shuffling" action system which allow players to act out-of-order and yes, it is often useful!

Stone age, by Bernd Brunnhofer it's a twist of the same problem. Again, no killing involved. The main difference is that there are really no movement costs (units move just for visual aid), they often have a chance to produce. Resource competition is no more driven by a production card but instead by a limited set of production slots. It's really more complicated than that.

Agricola (already mentioned), by Uwe Rosemberg is quite famous (even cited in XKCD). I guess I'm the only one not liking it as it gives pro players an extreme advantage compared to newcomers. I still have to remember what cards are supposed to be useful, let alone understand how most cards interact with each other!
In a certain sense, Stone Age is a streamlined Agricola, the difference being an extreme amount of emergent complexity, a richer resource set and a scarcer amount of resources. Agricola is a two-phase game:

• Players choose their advantages. This is basically playing poker, except every card is unique, you have to figure out what to pick up in advance.
  
  
• The game itself.

It is more difficult to understand and has more emergent complexity. I have played it for years and I still have to understand how people can do that in their spare time. To me, it is as fun as solving a 8x14x3 matrix. Or hunting a bug in a dynamically generated shader with dynamically streamed resources...
But I admit it has extreme strategic elements.