The 'social' skills (Diplomacy, Bluff, Sense Motive, Intimidate) are broad enough to cover all 'non-combat/roleplaying' situations.
Since the remaining stats/skills/systems are generally used for combat, I'd say that D&D is primarily a combat oriented game.
Well, I'll even disagree with that as a premise.
First, you missed several of the social skills: Animal Empathy (hey, it's limited but it's social and charisma based), Gather Information, Innuendo, Perform, and Speak Language. That brings the total number of primarily social skills to nine.
Of the remaining skills, none are directly combat skills and only a few have real use in combat. The ones that are directly combat skills are Balance, Bluff, Concentration, Escape Artist, Heal, Ride, Spellcraft, Tumble and (in some cases) Use Magic Device. That brings the total of skills likely to be rolled in a combat round to nine, and some of those (like balance, bluff, ride and use magic device) are very dual purpose.
The remaining skills are 'life skills': alchemy, appraise, climb, craft, decipher script, disable device, disguise, forgery, handle animal, hide, intuit direction, jump, knowledge, listen, move silently, open lock, pick pocket, profession, read lips, scry, search, spot, swim, use rope, and wilderness lore. None of those are what you would call combat skills, useful though they may be. Even if we count move silently, spot, listen, and hide as combat skills, we are still left with more non-combat skills than combat skills.
So just counting skills, D&D is not primarily a combat game. D&D becomes a combat game because that is what people expect and that is what both DM's and players prepare for; but, that doesn't mean that is all that people want or expect.