Lumens per Watt.
Your MagLite single-AAA battery version provides 40 Lumens for 2 hours with a 1.5V Alkaline AAA. An alkaline AAA is, say, 1 Amp-Hr. So that's ~60 Lumens/Watt which is a credible for consumer LED technology.
I could not find specs on your Eveready single-D but found a Ray-O-Vac single-D flashlight providing (only) 9 Lumens but running for 160 hours. An alkaline D is, say, 17 A-Hr. So that's also about ~60 Lumens/Watt (imagine that!).
Are you really asking how does a white LED operate at 1.5V with NO electronics? As RRMAN says, are you sure there are no electronics? You can make a very compact circuit to step-up a 1.5V battery to the voltage that drives a typical White LED. Or, like a blinking LED all-in-one package, you can embed more than the light-emitting part into an LED.
As I see it, for a flashlight which uses a generic alkaline battery which droops in voltage essentially as soon as you put it into service, you want some kind of electronic power management circuitry to regulate power into the LED as the battery voltage drains/droops.
I'd be amused to see the business model of a technology company that thinks it wise to develop a White LED that intrinsically operates between 1.5V down to, say, 1.0V to put in a flashlight driven by a single-cell (1.5V) battery. Just my opinion, but I would not buy stock in that company.