You sound like you're looking for something like Jones'
The Art of War in the Western World:
http://www.amazon.com/Art-War-Western-World/dp/0252069668
Or just go there and follow Amazon "related" links.
Jones is of the "very broad" school of military history. It can be a little bit dry, but it certainly tries to be comprehensive: It's like Civilization in that it starts with phalanx and then moves slowly forward through the history of strategy and tactics.
You might like the works of John Keegan, another famous military historian who takes a general approach. He's got a History of Warfare that's like a lighter-weight version of Jones -- I might recommend starting with that, actually. His one-volume histories of WWI and WWII are probably decent.
Keegan is British, so it wouldn't surprise me if his histories were heavy on the Western front. If you want the actual history of WWII you need a history that's more about the Eastern Front, which is pretty much where the war in Europe was actually decided. Unfortunately, the history on that subject lags decades behind, because the surviving Germans didn't exactly want to dwell on it and the Soviets weren't exactly forthcoming. (Many of the key Soviet figures either got disappeared by Stalin or lived under the constant fear of being disappeared by Stalin.) I'm not sure what the best current general history of the Eastern Front is, but I do know that the big Western expert on the subject is David Glantz, who has spent the last twenty years digging through formerly-sealed Soviet records of enormous battles that were covered up for years. I'd probably start with:
http://www.amazon.com/Slaughterhouse-Handbook-Eastern-David-...
because I don't know any better and it comes up first on Amazon.
If you want something written by a gamer try the works of James Dunnigan, founder of SPI and author of a whole pile of famous simulation board games. I read most of his Dirty Little Secrets of World War II and it was interesting. A much breezier style than the heavy-duty military historians. And he's got books that cover contemporary military stuff as well as history.
Nobody should read about war at the 10,000 foot level without also reading about what it's actually like on the ground. Obviously, the great modern literary works on the subject are Slaughterhouse Five and, even more so, Catch-22. In the realm of nonfiction, Fussell's Wartime was interesting, but it led me to Eugene Sledge's With the Old Breed: At Peleliu and Okinawa, which is even better: a very good book by a guy from the front lines in the Pacific who is not shy about telling you exactly what went on. Comes with an endorsement by PG! (from the last time I mentioned it on HN.)Don't read it over lunch if you're squeamish.
(I haven't actually read some of these, but my dad is a military boardgamer and military history buff. He's got several bookshelves packed with books like these.)