Campbell said:'Kill dudes and steal their stuff' isn't really that strong of a defining trait for a role playing game. A large number of RPGs which are not D&D also emphasize combat and looting. Even those games that don't emphasize pillaging tend to have a good deal of murderizing.
As far as classic game play goes I see some elements of 4e that are tacit rejection of classic tropes. While D&D has always been driven mostly by game play elements, D&D game play as conceived by Arneson and Gygax focused on a structure that was reminiscent of extended war game campaigns where attrition, logistics, and preparation played a much larger role than they do in 4e. Classic play also focused more on adventuring and world building than the current paradigm does. World fidelity was considered a crucial element of play. There wasn't very much attention paid to the creation of a satisfying narrative or action oriented play. Some critical components of classic play include:
- Adventurers lived in a dangerous world where life was cheap.
- It was often assumed that PCs would have a litany of henchman and many players ran multiple PCs.
- Direct combat was rarely seen as a positive occurrence. You were expected to find ways to deal with creatures without putting your life on the line.
- PCs started out as normal folk and grew into something greater. They were still not special (no protagonism).
- Keeping track of things like arrows, spell components, and rations was considered a critical element of play.
- PCs were often out only to serve their own ends. Heroism was not assumed.
- Preparation and strategy were more important than combat tactics.
- Attrition of resources was a critical element of play.
4e basically embraces a more action adventure oriented approach that assumes a certain degree of PC protagonism. It also places the importance of the creation of a satisfactory narrative above world building and modeling. Additionally there is further emphasis being placed on each individual encounter serving as challenge (tactics over strategy). It continues a process that started with AD&D 2e material and continued with 3e. The difference this time is that Wizards has basically abandoned the incremental approach. They are creating an edition that matches their vision of the way D&D should be played without looking back and taking half measures. They did not construct a list of sacred cows this time around. That is a huge difference.
All these things you list as the classic elements of play are reasons I don't play the classic versions of the game anymore. Even when I was playing BECMI and AD&D 20 years ago we never had loads of henchmen and when was avoiding monsters ever the better route? you didn't get XP for that

And for the people who mention people not even being able to keep track of 5 abilities or remember rather simple rules like movement, yes I know it's a social event, but it isn't hard to learn these rules. If you can't remember a few simple abilities should you even be playing D&D? Not to sound elitist b/c I'm far from it, the people I've gamed with in the past who had problems like this were either too lazy to read or were just kind of there and didn't really care about what they were doing. I just don't understand spending a lot of time doing something if you don't enjoy it, so I prefer everyone I game with actually enjoys what we're doing and does the modicum of reading needed to figure out what they're doing with their character.