Keep in mind what it did compared to other WWII shooters.
For starters, half the campaign was set in the Pacific, which remained a mostly unexplored theme in WWII shooters. Medal of Honor touched on it in Rising Sun and Pacific Assault, and Battlefield had maps from it in BF1942 (BF1943 hadn't released yet), but not very many people played any of those, and Rising Sun was received horribly so we could also exclude that if we wanted to, and BF1942 didn't actually explore the Pacific side of the war so we could also exclude that. There were some other minor games set in the Pacific, but they weren't well-received or weren't well-known. Basically, outside of Medal of Honor: Pacific Assault, World at War was practically the first popular WWII shooter to be set at least partially in the Pacific, and I'm willing to bet it was the first time a vast majority of players had played a competent game set partially in the Pacific.
Second, most WWII shooters, and most popular military shooters for that matter, were T-rated games at that point. Brothers in Arms was the only major franchise that was mostly M-rated, and at that point CoD only had one M-rated game (CoD4). Battlefield wouldn't go M-rated for another year, and Medal of Honor would do it a year after BF. Basically, there weren't a lot of gritty military shooters at that point, and the one franchise really pushing a more mature experience (Brothers in Arms) was the least well-known of the major ones and likely not played by most people. World at War basically offered many people their first look into a gritty WWII shooter.
Finally, up until that point, very few WWII shooters, or military shooters in general, gave a look at the war like it did. Rather than painting it in the heroes-vs.-villains way like most military shooters, even the more mature ones, had up until that point, World at War basically painted both sides as killers we aren't really supposed to worship. Granted, on the Allied side, the Russians received this treatment more than the Americans, but there were still hints of it in the American campaign, regardless of the more positive portrayal of Americans. It offered the player the opportunity to make a few moral choices in the Russian campaign that would ultimately determine how one character viewed the player, but as far as I know, the best you can do is make him confused about whether the player is a sympathetic hero or a merciless killer, which pretty much sums up the game's tone very well.
Obviously, over the last 5-6 years, some of its strong points in 2008 have been lost. With shooters basically all being gritty and trying their best to use shock value, the grittiness has been lost compared to what it would have been like five years ago. Also, plenty of games, especially Spec Ops: The Line, have done a much better job with its theme so the impact is less meaningful now than it was a few years ago. Really, most of the charm it had back in 2008 has been lost, but back in 2008, it was a surprisingly fantastic campaign, especially by Call of Duty standards.
