I'm not 100% sure but I believe he means the mechanics-first design of 4e versus much of the story-based design of earlier editions.
4e designed around the basis of the mechanic. As always, there are exceptions and there was quite often a story-kernel at the basis of the design, but it was often much narrower than the role of the class in the larger world.
The warlord is one example of this, being designed first and foremost around the concept of the martial leader that can grant attacks, damage, and movement while also healing. When you describe a warlord first and foremost you describe what he does in combat and his mechanics.
Ditto the avenger which was based around the oath mechanic, the idea of a Batman character that fights alone while being part of a team, and the visual of a lightly armoured sword wielder.
5e is starting with the story first, describing what the class is in the world, what its role is, how it is unique and then looking at mechanics. Or so we've been told.
When you start with the story, you'll always get a good world hook. And there's nothing preventing you from making equally unique mechanics and designing an awesome class.
When you start with the mechanics first, sometimes you're going to get a good world hook and sometimes you're not. Few of the 4e classes really stand out for their flavour. The battlemind is a mass of story contradictions completely divorced from its flavour. The seeker and runepriest overlap with the ranger and the cleric. The battlerager fighter should have been a defender barbarian.
But I disagree with GX.Sigma that mechanics first cannot lead to good story and classes. I thought the swordmage worked fine, and the warlord does still deserve to be it's own class.
I just reject the whole notion that 4e somehow is designed in any fundamentally different way than any other edition. Do you think that Vancian casting wasn't designed as it is for gamist reasons? Of course it was. They had a mechanical concept of spell slots which was intended to limit the effectiveness of wizards and make them play a resource game, and then they found a suitable explanation for it. The very fact that DIFFERENT explanations were offered in each edition makes this abundantly clear. The cleric, same thing. Do you think the armor and weapon restriction rules were made up for story reasons? Of course not, fantasy is replete with sword-wielding wizards and clerics being forced to use maces makes no story sense at all. The very existence of rules like hit points and armor class clearly are entirely gamist, and the granting of d8s to fighting men and d4s to magic users has nothing to do with 'story', it is purely a gamist device to balance the classes.
Now, I'm not saying these mechanics weren't partially selected over others because of their suitability in story terms, undoubtedly they were, but only after they were found mechanically suitable. In truth game design is not a linear process and doesn't proceed from concept to mechanics or vice versa. I am relatively confident that the 4e designers of the Avenger class had a concept in mind, you even named it right off, Batman. Maybe they used a different one, Batman is a bit outside D&D genre, but Zorro, D'Artagnon, etc could all serve as adequate models. The point is the mechanics may have been some idea that was lying around, maybe someone thought of that first and then thought AHAH! That will work great for an Avenger! Chances are the original kernel of the idea for the mechanic was itself inspired by the thought of a lone avenging combatant, and may have been quite different from the final version. Surely there were some tweaks along the way. I think this was true with all the 4e classes.
I think what people mistake in all these cases is tight mechanics. There IS a desire in 4e to take account of the GAME implications of things. It isn't 'mechanics first', it is "no, we aren't going to just make up any story that steps all over the whole game just because we could". Wizards don't get to be super powerful "just because", etc. Honestly, this is very much like the way the designer of OD&D made 3 fairly balanced classes of dungeon explorers.
There's another problem with this. SURELY very many of the 3e classes were designed to leverage mechanical concepts, certainly to the same degree that 4e classes were. If you are critical of 4e on this score you must be double critical of 3e.
Chainmail was a game of dungeon exploration. D&D was that for thirty seconds and quickly evolved. It did not take long for D&D to move beyond the dungeon, for worlds to grow larger and grander. For people to start questioning how the world the mechanics were creating might actually work and interact.
Eh, just to let you know, not that it changes anything, Chainmail was purely tabletop mass combat rules, there was no exploration. It wasn't even an RPG. The 'fantasy supplement' at the back of the chainmail book had some rules for a wizard (basically a cannon), a dragon, and some other 'fantastic' (basically Tolkien) races. Presumably you were to use these to reproduce battles from LotR or similar sources. There was an optional rule in there to allow heroes and monsters to fight 1-on-1 if they happened to meet on the field of battle. A normal 10-minute Chainmail turn was divided into 10 1 minute rounds and the two figures when head-to-head using a special table. This table was later used as one of the combat options in OD&D, before Greyhawk permanently replaced it with basically the current system using d20.
While of course people started to do other things besides JUST dungeon crawl pretty soon, the VAST majority of the game, right up to the present, has always been focused pretty steadily on dungeon crawling. Practically every module out there from TSR is mainly a crawl of some sort. Most of the WotC modules are too. Very little thought was ever given to what magic or other class features would mean in the wider world. They were designed specifically to allow for the creation of a mixed party of adventurers exploring some sort of underworld, or now and then some wilderness or town. As long as the rest of the world was mainly kept as a sort of vague backdrop and supplier of plot hooks and such it worked pretty well. As soon as you wondered who actually made magic items, why wizards didn't just open banks or betting parlors, how a town of 3000 people could support a thieve's guild, etc it worked OK. Gary even provided enough of a ready-made answer for questions like "where do orcs come from" that most people had no real trouble focusing on their character and not worrying about the rest.
And while the game was simple now, you can't go back to that. The genie is long out of the bottle and people do wonder how classes interact and affect and alter the world. The world consequences of clerics with cure spells has been known for twenty-five years and was part of the basis of the original Dragonlance world. We cannot design like it was 1974 anymore.
Well, I have 2 answers to that. First of all, sure we can. I have no illusions that I or anyone else is capable of knowing what the consequences of fantastical things would be in the world, especially some other world than our own. Thus I don't really think we CAN do any other sort of design. Nor do I think some other sort of design would be that interesting. Finally, I just don't think the Warlord PC is that big a deal. He's the Sergeant Rock of his world, there's really only a few of him out there, and most are far less capable than he is. Your average sergeants and knights and whatever? They can't do Inspiring Word. Even if they get that power now and then in a scenario, that doesn't even mean they could NORMALLY do it. It means in this dramatic situation they managed to do it once, maybe.
Overall, I'm perfectly happy if there are other alternatives than healing for a warlord, but I want to see that as an option, presented along with the other options. I want to see a 4e type of play being supported. One where the party can have a variety of compositions and its possible to do some variations on the classic D&D tropes.
I mean really, for all people seem to have this idea that 4e is 'not as flexible' it is MUCH easier to do things like Dark Sun, or Dragonlance, using 4e than with earlier edition rules. I find it interesting right off that these 2 major setting variations BOTH zeroed in on clerics as a major aspect of the game to change too. NOTHING can be more evidence of 'not thinking about world consequences' than the CLW spell itself.