The NYT corroborates Engadget's previous Apple TV leak, saying that Apple is working on re-designing the product with some kind of iOS operating system instead of what it uses currently. However, the NYT hints at something more: an actual TV.
It's all very vague and hinty, but if you read into it you can see that there's some talk of a physical television instead of just a headless box.
They also said Apple might base a new television design on its iOS operating system, which is on the iPhone, iPad and iPod Touch.
Also, the NYT says it's not being designed by the current Apple TV team, but by another design group entirely. That could either mean just a radical change in the box shape, or an entirely new type of product (a TV).
It only makes sense for Apple to re-up on their living room efforts after Google TV showed that it was possible to insert a computer-like product into the living room and have it not be so computery that it be unusable, but not so gimped (like the Apple TV) that it couldn't really do much except suck down one company's offerings. And with iPad, iPhone and iTouch, Apple's got very good interoperability devices already in those houses.