Absolutely this.
Likewise with the "any means necessary" style of play - if ticking off orc henchmen is no different from ticking off arrows in a quiver than Robilar's conquest of the ToH, while perhaps distasteful, is nothing very special in comparison to a 4e wizard solving a problem with rituals while the player dutifuly marks off the components used.
This is all about the ingame fiction. It doesn't tell me anything about playstyle.
For instance, if the game was HeroQuest revised, or Burning Wheel, then both hacking through the security system, and stealing a bomb to knock out the grid, might be resolved with a single check. (If framed by the GM as simple contests.)
In a 4e skill challenge, it is taken for granted (by me as a player/GM, but also I think in the rulebooks) that the players will try to leverage and twist the fiction so that they can bring their PCs' best skills to bear. In my Torog example, for instance (linked above), you see the sorcerer using his magical fire spell to melt the ice, thereby leveraging Arcana skill. (Whereas a natural fire would leverage the PC's noticeably weaker Nature skill.) Likewise the ranger flies on his carpet (leveraging an excellent Acrobatics skill) rather than running across-country (the PC's Athletics is mediocre), and vice versa for the fighter.
Looked at through this lens, what I see in your example is that Team A have stronger stealth/bluff, while Team B have stronger break & enter/demolitions - so each team is playing to its strengths.
The only approach to RPGing that doesn't permit this sort of play - that is, players leveraging the fiction to deploy their best resources - is railroading/Adventure Path play. (I disagreed upthread with [MENTION=22779]Hussar[/MENTION] that this was what Pulsipher is getting at with ID vs WF, but it might be apposite for trying to make sense of this CaW/CaS thing.)
There are multiple things going on here.
One is about resolution techniques. In Robilar's case, the GM is "saying yes". The GM could, presumably, turn this into an exciting game of psycho-social tension among the cadres of orcs. (For instance, Gygax's DMG has rules for loyalty checks that would be relevant in these circumstances.) But for whatever reason has chosen not to.
A game could be resolved in just the same way without the orcs - for instance, replace the orcs with a standard procedure involving 10' poles, a flying thief on a rope with lots of Wish spells for resurrection, etc.
Another is about the fictional stakes of the game. The player who finds the whole thing boring was looking for a game about dramatic tomb-looting (Indiana Jones style? or something pulpy like that.) And has instead received a game of resource management in which it could just as easily be about supplying drinks to customers in an inn as feeding orcs to traps in the ToH.
There are other ways in which the differences in desires could be described, too.
But I'm baffled as to why anyone would think that "combat as war" and "combat as sport" are useful ways of drawing any of these contrasts.
I definitely think this is part of it. What sort of colour/flavour do we want? (Orc slaves? Tombs? Heist? Blowing things up?)
Who frames (and reframes) scenes - GM or players?
What sort of resolution system do we want (resource management? high gamble, like SoD, or low gamble, like 4e? etc)
How important is fictional positioning to resolution?
These are all interesting aspects of RPG design and play, but I don't see any particular connection to war or to sport. As Hussar says, the whole game is artifice, and we're talking about the ways in which it is to be undertaken.
