Yes, he is finished in politics because he has too many scandals to be able to survive his term as governor. He may be impeached and he was beaten easily when running for president in the Republican primary. He latched onto Donald Trump and will ultimately have to look for work elsewhere.
Chris Christie has done very, very little to improve the NJ economy. He has not reduced the State Spending. He failed to fund the state pension, despite his own agreement with the legislature to do so, and kick the state pension insolvency can down the road. He did nothing while counties and municipalities continue to add more people to the pension plan. His 2nd Amendment stance/advocacy has been terrible. He allows a municipality to use eminent domain to condemn a successful privately owned airport.
Christie abuses his political power. People know this. Christie has used political power to back up traffic on a highway so that political adversaries are inconvenienced. That is a dangerous person to vote into office, and voters know it. He lost the public's trust a long time ago. It is time for him to retire and eat Krispie Kremes.
There is no way to know if Chris Christie is finished in politics, but politicians tend to find ways to stay in office. Regardless of his current approval rating, Chris Christie can certainly make a comeback. Many politicians have done more unbelievable things. He may be elected as a Congressman next if not reelected.