'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.