There is still a resource game, just symmetrical and same-y between Classes and as much focused on short-term as long-term resources (which was continued into 5E with short rest mechanics and Classes). The lack of a dynamic resource game was unfortunate.
That resource game doesn't depend on tracking time as Gygax describes it. It depends on knowing when an encounter ends; and knowing when the PCs take a long rest.
You can amp it up if you want to - nothing in 4e
stops you from tracking rations, for instance, or tracking travel time across the wastelands - but the game doesn't require it. For instance, a trip across the wastelands can be framed as a skill challenge, and thus a single encounter and so no reuse of encounter powers, and the game will work fine - in fact, I would argue,
better than it would if you actually tracked the time Gygax-style.
In that sort of play, the passage of time becomes simply colour. (There also needs to be colour to explain why the PCs can't get a proper extended rest. At heroic the colour I used was swamps, irritating insects, rain, etc; at paragon and epic the awful life-sapping environment, and chaotic forces, of the Underdark or Abyss or whatever horrible place the PCs found themselves in.)
And seeing as how the resource game was up until then a pretty significant and important part of the overall game, it's small wonder 4e with its removal of this aspect of play got the less-than-enthusiastic reception it did...
I'm not really that interested in 4e's reception. I've participated in endless threads about that, and have expressed my own view - namely, that there is only limited market demand for a RPG that combines the indie sensibilities of Maelstrom Storytelling or HeroWars/Quest with the mechanical heaviness of Runequest or Rolemaster - but ultimately I don't pick what RPGs I play based on how many other people like them. I pick them based on my own view of what they have to offer me in terms of play experience.
But this is one of those respects where either 4e is the same, or different, but can't be both at the same time. If I'm in fact correct that 4e doesn't have a resource game like AD&D does, then I'm also correct that Gygax's injunction that you can't have a meaningful campaign without tracking time doesn't apply.
Of the seven systems for which I currently have active campaigns, or have run relatively recently, three require tracking time because it is an important resource and four treat time in the sense Gygax cared about it as simply colour.
Time is part of resolution
AD&D: healing, travel, wandering monsters, rations, and probably other stuff I'm forgetting, are all related to the passage of ingame time, and just as Gygax says managing time is an aspect of skilled play.
Burning Wheel: healing, training, and maintenance checks, plus some other less crucial stuff like crafting, all have costs in time, and so players have to make trade-offs (eg spending a lot of time on training will leave you not earning money, which then leaves you vulnerable to Resources depletion when it comes time to make a maintenance check). The GN also has an informal liberty in scene framing that follows from the passage of time: the more time the players spend having their PCs do stuff that doesn't thwart their nemeses, the more the GM can reframe the background situation adversely to the PCs without being unfair in doing so.
Classic Traveller: consumption of fuel by starships, healing, training, living expenses, saving throws to avoid the decrepitude that comes with age - all this is based on the passage of time. Given that living expenses probably won't be a big deal for most PCs, the main part of the game that makes time a resource is trying to earn enough money to meet repayments on the starship loan. Other than this, the passage of time isn't so much a resource as a bakcground thing that triggers these other happenings. (Of the systems I run, Traveller is the most simulationist.)
Time is really just colour and perhaps a bit of pacing
4e: recovery rates matter, but that can treated purely in terms of GM-mediated game play ("OK, now you get a short rest"; "OK, now you can take a long rest if you like" - at least at my table the GM-mediation often bleeds into straightforward group consensus). The connection of these rests to the passage of ingame time is pure colour, and not itself an input into resolution.
MHRP/Cortex+ Heroic: everything is measured in Action Scenes and Transition Scenes, and time is purely colour. We've had transition scenes that correpsond to1 taking a rest in a dungeon room and transition scenes that correspond to spending days or weeks just hanging out. In mechanical terms those are identical.
Prince Valiant: time is just an element of colour that can alsoe be used for framing by the GM - eg as GM I'm within my rights to say "OK, you've been travelling through the forest for a while and are feeling hungry - let's have some Hunting checks to see what game you're able to catch" and if they fail the checks then I can impose Brawn penalties. But I'm equally entitled just to narrate "OK, after a week or so of riding you're back in Warwick." It's all GM-side management of pacing, colour, a fair sequence of challenges that evoke knightly adventure, etc.
Cthulhu Dark: when we played a session of this system, I had initially thought about using an old CoC module I have (the Vanishing Sorcerer) but a quick read of it suggested it was pretty bad and we could probably come up with something better spontaneously, and so we just made up the fiction as we went along. The passage of time was simply a matter of colour: I think our adventure spanned about 3 days, and at least one night passed without incident ("OK, it's tomorrow, who's doing what?") while one night invovled fitful dreams and then the PC waking up with her house on fire (which triggered some action declarations and checks). We didn't get to the point where the recovery of sanity rules kick in (at 5 pips on the sanity die, and we only got to 4), but they depend not on spending time as a resource but on performing certain actions.
There is no general rule that time has to matter in RPGing; and no general rule that it has to matter in RPG systems that involve player-side resource management: 4e and MHRP/Cortex+ are both systems where the players have to manage resources, but the management is locked into the former's recovery structure and the latter's scene structure, neither of which depends upon tracking the passage of ingame time or treating
it as a player-side resource. (Prinve Valiant does have player-side resources, but equipment and money are completely time-independent and closer to GM largesse, and Storyteller Certificates are also time-independent and utterly GM largesse.)
Finally, here's my least favourite way of handling time in a RPG:
treating it as a player side resource while in fact everything that it matters to is managed by the GM offstage. In my personal experience, traditional FRPG asymmetric resource suites are especially prone to push play in this direction if the game has any sort of story/pacing dynamic to it (ie it's closer in tone to Dragonlance than Tomb of Horrors). My own personal experience with this is mostly from Rolemaster: the AD&D games I've run with that sort of dynamic have involved all "martial" parties and so haven't raised the asymmetry issue. In my first long RM campaign the group hit upon it's own solution - over time everyone played a spellcaster. In my second long RM campaign we changed various system aspects and play conventions to produce the result that, basically, a "martial" PC was pretty much as effective as a nova-ing caster.
But my subsequent experience with 4e and other systems without this headache mean that I would personally never go back to such a system. (The few times in the past few years when I've run a session of AD&D have been pure dungeon-crawl, which doesn't have the problem because there is no pacing to manage in such a game.)
