Regarding 4e, I consider its design goal to be "rules first". Its highest priority was to create a game engine with balanced mechanics.
A secondary goal was to "consolidate" the sprawling D&D traditions into "salient" concepts. This resulted in mostly lumping different things together (such as Dray becomes Dragonborn), but sometimes splitting them (such as splitting Elf into three separate races − Elf, Eladrin, and Drow − each one a consolidation of many different kinds of Elves). This remix of D&D traditions generally worked well, but there were legitimate disputes about specific examples (such as Elf).
A less important goal might be the most consequential: "everything is core". If it exists somewhere in 4e, then it is true everywhere in 4e. This led to the updating of every D&D setting to include every feature in 4e, such as introducing Eladrin to Dark Sun (in a way that works really well!). This occasionally produced outcries especially from Forgotten Realms fans, when the 4e update was moreorless a wreckingball obsoleting and obliterating the extensive and intricate "canon" of Forgotten Realms.
I would describe 4e as:
• mechanics first
• concept second
• flavor last
The 4e mechanics were intentionally designed to invite players to reflavor any mechanic.