Splash:
Nice catch! I'm saying that with reference to my own intention of understanding the discussion in Romans 6.
Incidentally, in the most recent NWT the brackets were taken out. In the previous edition and in the WT Library CD "his" is in brackets. (Often times a verb has no subject and a translation will insert a pronoun according to the inflection of the verb. Off hand, I'm not sure if that was the intention here [in the NWT] or if the intention was doctinal. I would venture to say, based on how the Society views the verse, that it is doctrinal. But I'm just conjecturing.)
But either way, "his" changes the meaning of the argument in Romans 6. If you look at the context beginning in verse one, Paul is talking about "sin" in a general sense, as a principle ('sinfulness', as it were), not an individual's particular sins that he may have committed. And that fits well with the idea that "he that has died" is referring to a believer that has been baptized.
Thanks again for the good eye.
Take Care
Edited to add:
Just looking at the context and verse 7 again, I feel quite confident that "sin" in verse 7 is abstract, not, as you said, a particular history of sin. The article before "sin" is genetive, singular, feminine.