I think the tactical depth of 4e is a bit of a chimera as PCs win pretty much all the time.
In a 4e game the DM has a lot of control over the difficulty, and the players have a lot of control over the amount of risk they're willing to take. Assuming your DM is capable then you can have a quite interesting time finding out HOW the player's win all those fights.
I agree with AbdulAlhazred here.
I also have doubts about the "combat as war"/"combat as sport" distinction. To me it seems to be about mechanical features of early D&D rather than about the content or character of the fiction.
For instance, early D&D had fairly tight resolution mechanics for "I cut his head off with my sword": roll to hit, roll to damage, adjust hit point totals, etc.
Whereas it had very relaxed mechanics for "I slip poison into his drinking goblet": perhaps a DEX check, and poison bypasses the hit point mechanic.
You could easily resolve sword swings the same way: state intent, make an appropriate check, and then narrate the outcome without anything like a hit point mechanic to constrain the scope of success and force multiple action declarations to get total victory. Burning Wheel permits this: "I cut his head of with my sword", make a simple check, and if it succeeds the enemy's head is cut off! I've allowed this in 4e too: "I kill him with a Magic Missile", make an Arcana check, and on a success the NPC is "minionised" and dies to the MM's autodamage.
Sometimes, though, it's fun to have a hit point track, or some analogous device, that forces the resolution to become a bit more intricate and gritty. That's why not every 4e combat is fought against minions, and why some non-combat challenges are resolved as skill challenges. (
Here's an old thread with some good discussion of the latter point.)
In my experience, those who vigorously advocate the "combat as war"/"combat as sport" dichotomy are generally advocating for player control over certain aspects of scene-framing (or, rather, scene-reframing) with that control mediated fairly loosely via free roleplaying that takes advantage of gaps in the system's formal resolution mechanics. Although many of those advocates don't seem to have a lot of familiarity with variations in the mechanical design of RPGs, and so tend to run together the metagame element of their advocacy (which I've just described) with claims about the imaginative nature of the fiction that is generated by pursuing their favoured approach to action resolution.