It feels like people are going off of the thread title and reacting without reading the actual quotes. He didn't say that the Kings are running out of time, but that he and the remaining Cup-winning veterans are running out of time. He's not wrong. He and Kopitar, especially, had very good seasons, but may not have very many of those left. He just wants the Kings to accelerate the rebuild a little so that they're competitive while he can still contribute to it.
Also, it's not as if he volunteered this opinion. He was asked in his final media interview if the Kings should spend this Summer to bring in pieces and he gave his honest answer. The reporter even pressed him to elaborate. It may've even been the same reporter who wrote up that NHL.com article, perhaps trying to coax some juicy quotes out of him that would make for a good article. Doughty fell for it.