Well then, let's clear up some terrible misconceptions about starcraft first, because your question is indeed a loaded one. The primary point of all of my arguing is to try and clear the stupid myth that starcraft is a clicking contest, first and foremost. My mentioning of Company of Heroes is simply because it's probably the most common "Starcraft is a clicking contest, here's a real strategy game" example folks choose.
Secondly, to answer your question about the strategic depth, here goes:
Firstly, Each race is vastly different, a fine way to exemplify this is to note that in the professional scene, there are no random players, despite there being no provisions against it (and indeed, in the early years random players existed, much like SC2 now). This comes from the fact that each racial matchup is unique in and of itself, leading to 9 matchups to learn in general, with very little overlap between the two in thought processes, unit compositions, pace, and general ideas.
Another major facet is the massive role in the game played by economy. all things related to your economy and the use of the money you get from it are called Macromanagement. Macro is huge, in that it's a system with simple rules, but with a complex and constant effect on the game; Workers are some of the most crucial units in the game, making worker harassment, constant worker production, and ample base defense plans big deals in the game. This is admittedly APM heavy, but if that were all you had to do in the game, anybody could do it.
Unit control, or Micro, is another major part of the game, and it's not as simple as just controlling the groups with the limitations of 12 unit selection groups, but micromanagement tricks, positioning, map considerations, spellcaster control and spell placement, all of which has a fairly low room for error. It's in fact the ease with which you can mismicro a unit that makes the game exciting and unpredictable even after ten years. Again, if that were all you had to do, the game would be simple. (A fine example of a game that does so is Warcraft 3, though the depth of it's micromanagement is at the very least equal to Starcraft's, much to some fanboys' chargrin)
Then we throw in other big factors, such as scouting, decision making, the armor system that is much like starcraft itself in that it is simple and extremely effective in it's depth in context, and playing for or against game trends.
The worst part of everything I said above? I massively simplified each aspect, and if I were a more diligent person, I could write you entire articles surrounding the endless rabbit hole that is starcraft strategy.