Many factors play into this. Sadly, simple google searches do not get me much data that isn't noise regarding the very question you are asking about. That said, I am a Program Manager working on many varieties of IR lasers, so I will attempt to give you information as best as I can explain it.
First of all, anything people "feel" in their eyes is purely psychosomatic. The retina does not have any pain sensors in it (the linked diagram shows no nerve endings in the eye). Any eyestrain is more than likely from spending hours in front of a TV set playing a video game as opposed to the laser.
The laser itself is 780nm (visible light ending at 760 nm, thus making the Kinect laser very short wave IR, or SWIR). Furthermore, it is not columnated, but rather diffused so that it covers a wide area. The power of the laser ends up at less than 0.4 µW once it actually reaches you, so you have even less reason to worry. It is rated as a Class 1 laser device, which means the maximum emitted power of the laser is <25 μW, spread out over a circle detection area measured in feet as opposed to an aperture of less than 1 cm. This amount of power, according to current medical and physics knowledge, is safe.
For the sake of comparison, sunlight is one kilowatt per square meter and perhaps 5% of that is near infrared i.e. 700 to 1000 nanometers. Just going outside will expose you to much greater power densities of SWIR than the Kinect.
As to the way the Kinect physically generates the laser, the IR laser diode itself is capable of emitting 60 mW at 830 nm. Should you break or remove the diffuser, various optics, and then stare into the laser emitting diode directly, you will cause retinal damage. However, the series of steps required to do that would indicate a willful intent to cause self harm, and be beyond simple mechanical failure.
EDIT TO ADD: As previously stated, in order to be classified as a Class I laser, the emittance must be <25 μW. The reason that the diode generator is higher is because the optics required to create the dispersal pattern reduces the efficiency. Any time a laser passes through any optical element, you lose power. The beam divergence will also play into this. If the M2 (M squared) is close to 1, you will have problems. I have not found any measurement of the Kinect M squared, however, since it is already set to diverge, that optical path is established before it even leaves the device. This ends up reducing the ability of the laser to be focused in any meaningful way on your retina.
I would call into question the methodology that people claim in measuring the power from this laser.