Research operationalizing so-called strategic thinking? Is there contemporary research in trait psychology, which attempts to operationalize the structures behind a strategic thinking style? I'm thinking of a style of problem solving as taught in officer training, and to a lesser extent, manifesting in strategically-oriented games like chess. 

I realize that this sounds perhaps a little vague. However, in common usage it's not unusual to refer to a person's being a "strategic thinker" or a "problem solver". I wanted to know whether these traits have been studied or deconstructed in a more formal capacity, so as to define them in a manner consistent with trait psychology. 

Are there scientific definitions of strategic thinking with empirical support?
There is a large body of research on complex problem solving that is highly relevant to your question. 

The starting point of this research was a critique of classic reasoning and problem solving research which seemed to focus on very small problems (such as the Tower of Hanoi), which may not capture the complexity of many real world problems that people face. The initial goal of this research was to conceptualize the characteristics of such problems. 

In an attempt to find the common denominators of various definitions, Frensch and Funke (1995) define complex problem solving in the following way: 


  [Complex problem solving] occurs to overcome barriers between a given state and a desired goal state by means of behavioral and/or cognitive, multistep activities. The given state, goal state, and barriers between given state and goal state are complex, change dynamically during problem solving, and are intransparent. The exact properties of the given state, goal state, and barriers are unknown to the solver at the outset. CPS implies the efficient interaction between a solver and the situational requirements of the task, and involves a solver’s cognitive, emotional, personal, and social abilities and knowledge.


The method of choice to investigate complex problem solving has been to use computer-simulated microworlds to pose complex problems, such as trying to improve the success of a simulated city as its mayor, fighting a wildfire, or running a factory  (Brehmer &amp; Dörner, 1993, Dörner, 1997). In line with the definition, the performance in these simulations is determined in a complex way in that it is based on many decision variables, who are highly interconnected, and affect each other in a dynamic way. Furthermore, at the outset of the simulation, these variables and their relationships are intransparent and the simulation may be characterized by conflicting goals that have to be achieved by setting priorities and reaching compromises.

From this description, it may be clear that this research has focused more strongly on the "problem side". However, it has also explicitly incorporated personality and characteristics of the decision maker, such as motivation, certain (strategic) knowledge, and emotion regulation (see for example, Wenke et al. 2005). For example, much research has been devoted to the question whether the ability to solve complex problems can be distinguished from general intelligence. Some studies (e.g. Wüstenberg et al. 2012) suggest that even though performance assessed with in complex computer-simulated problems is highly related to intelligence, it can indeed predict behavior above and beyond IQ (incremental validity). 

References

Brehmer, B., &amp; Dörner, D. (1993). Experiments with computer-simulated microworlds: Escaping both the narrow straits of the laboratory and the deep blue sea of the field study. Computers in Human Behavior, 9, 171–184.

Dörner, D. (1997). The logic of failure. Recognizing and avoiding error
in complex situations. New York: Basic Books.

Frensch, P. and Funke, J. (1995) Definitions, Traditions and a General 
Framework for Understanding Complex Problem Solving. In P. A. Frensch and
J. Funke (Eds.), Complex Problem Solving: The European Perspective.(Hillsdale, NJ, Lawrence Erlbaum). 3-25. 

Wenke, D., Frensch, P. A., &amp; Funke, J. (2005). Complex problem
solving and intelligence: Empirical relation and causal direction.
In R. J. Sternberg &amp; J. E. Pretz (Eds.),Cognition and intelligence:
Identifying the mechanisms of the mind (pp. 160–187). New York:
Cambridge University Press.

Wüstenberg, S., Greiff, S., &amp; Funke, J. (2012). Complex problem solving — More than reasoning? Intelligence, 40, 1–14. doi:10.1016/j.intell.2011.11.003