The definition of manslaughter varies between states, and I am not a lawyer, but in general, criminal manslaughter charges only apply if there is an element of extreme negligence or doing something unlawful (like driving in an illegal manner) and causing a death.
For instance, there are accidents that cause deaths all the time; but they would only be prosecuted as manslaughter if someone were doing something considered inherently unsafe and unlawful.
If you run a red light, and kill someone in the process, it's possible you could be prosecuted for manslaughter, though even then you might not be if there could have been extenuating circumstances (sun in your eyes, etc).
In this case, there would only be a chance of a manslaughter charge if Uber were somehow being particularly negligent. In this case, it sounds like there was a human operator in the car, though the car was in autonomous mode. It's possible that the operator wasn't paying the attention that he or she should have been, or it's possible that even the human operator didn't see the pedestrian in time. It mentions that the pedestrian was crossing outside of any crosswalk, so it's possible that this was a tragic accident of them trying to cross a street with traffic without having been sufficiently careful.
On the other hand, it mentions a bicycle, but also says the victim was walking, which I find odd:
"Elaine Herzberg, 49, was walking outside the crosswalk on a four-lane
road in the Phoenix suburb of Tempe about 10 p.m. MST Sunday (0400 GMT
Monday) when she was struck by the Uber vehicle, police said."
Local television footage of the scene showed a crumpled bike and a Volvo
XC90 SUV with a smashed-in front. It was unknown whether Herzberg was on
foot or on a bike.
Anyhow, it is relatively uncommon for drivers to be charged with manslaughter in this country; they generally have to be doing something quite egregious, like driving drunk or driving at 90 in a 30 mph zone. Most of the time, the response to people being killed in traffic accidents is just that accidents happen.
Unless the operator was being particularly negligent, or there was some serious and known problem with the self driving car but it was put on the road anyhow, I doubt any manslaughter charges will be filed.
Remember, Arizona has explicitly been encouraging the testing of self-driving cars, so I expect that testing a self driving car, with an operator to take over in cases which it can't handle, would not be considered unlawful or extremely negligent. Maybe what the operator was doing could be, but we'd need more information before it would be possible to tell.