The graph you link to indicates Aclohol in one column, Traffic Collisions in another column, and a whole slew of other categories.
Traffic Collisions are at 43,000. (I would assume that drunk driving deaths would be included in this column, as opposed to death due to alcoholism being what is found in the Alcohol column) 9,000 is just shy of 21% of all traffic deaths. That is not insignificant.
However, DUI caused total just over half those caused by drug abuse (17,000), just under half those caused by STD's (20,000), just under 1/3 those caused by firearms (29,000) (side note: DUI's cause just less preventable deaths than homicide by firearm, and just more than 50% of firearms suicides), and is just over 10% of the deaths caused by alcoholism (85,000!).
According to your stats, there were 870,909 total preventable deaths in the US last year. That puts DUIs at 1% of the preventable deaths. If you exclude smoking and obesity, you have 324,000, of which DUIs' would be 2.8%.
There is not a single overall category that is less than DUI caused deaths. In fact there is not a single overall category that is not close to TWICE as many deaths when compared to DUIs. And overall, you are looking at 1%. Considering the homicide and suicide numbers are only with regards to firearms, and are not an overall total, I would have to say the DUI is pretty low on the list.
The only thing that I will give you is that that 9,000 deaths is right on par with how many deaths "studies" show are prevented by seat belt use each year.
(
Wikipedia Seat Belts)