The court also ruled that evidence Mr Dotcom and his co-accused said they were prevented from calling would not have affected the decision to extradite.
"We have now been to three courts each with a different legal analysis", Mr Rothken wrote on Twitter.
"We will seek review with the NZ Supreme Court", he tweeted.
Prosecutors allege that Megaupload, which once accounted for 4 percent of all internet traffic, generated more than $175 million in criminal proceeds from the exchange of pirated films, music and files. It has been called the "Mega conspiracy" after several companies allegedly facilitated, encouraged and profited from significant mass infringement of copyright.
On February 6, 2012, a U.S. grand jury indicted the group, and the USA has sought their extradition ever since.
"Many important cases in New Zealand are not won in the Court of Appeal, or in the courts below, but are won when they reach the Supreme Court, My case will be one of those", he said. "I will appeal to the Supreme Court".
Now, the final decision as to whether the Dotcom and the other men will be extradited rests with Justice Minister Andrew Little.
The latest ruling does not determine whether the defendants are guilty or innocent, merely that they can be sent to the USA to stand trial.
The court of appeal has now upheld a lower court ruling from 2017 which found that the extradition could take place. Dotcom has been fighting the extradition ever since the Federal Bureau of Investigation shut down his digital empire in 2012.
Dotcom disputed the court's interpretation of copyright provisions.
Obama was in the country for three days at the time.
Last year, police are believed to have paid Dotcom a six-figure sum in a private settlement over alleged unreasonable force.
"We are satisfied New Zealand law permits extradition for copyright infringement in the circumstances of this case", said the court's decision, by Justices Kós, French and Miller.