Generally speaking, we have a rule that "kol hayotzei min hatahor tahor, vichol hayotzei min hatamei tamei" ("that which comes from a kosher species is kosher, and that which comes from a non-kosher species is non-kosher"; see Bekhoroth 1:2). Since this new species comes from kosher and non-kosher species, there would be several potential halachic arguments that might be raised.
Would we consider it a taaroveth (mixture) of kosher and non-kosher? If that were the case, we would presumably be able to apply the rule of bittul b'rov/b'shishim/b'elef (annulment in a majority/1:60/1:1,000) inasmuch as the majority of the tissue come from kosher sources.
However, it's at best controversial whether a living organism could be considered a full-fledged ta'aroveth. While we are indeed strict with regard to animals that have been entirely sustained/fed with non-kosher (see e.g. Rama Yoreh De'ah 60:1), animals that even have been primarily fed non-kosher would not seem to be a problem. If genetic engineering is considered no more significant than feeding, it shouldn't be a problem.
One potential caveat to this reasoning is presented by the principle of davar hamaamid (see e.g. Rambam Ma'achaloth Assuroth 9:16), since the non-kosher tissue/gene causes the animal's dramatic growth-rate. A counterpoint to this line of argument would be that the actual non-kosher tissue that is added is presumably smaller than what could be discerned by the naked eye which may well remove from it any halachic significance (though this reasoning itself potentially opens up a Pandora's box of questioning...). Further, an animal fed primarily but not exclusively non-kosher is also arguably no worse in this respect.
Finally, from a recent New York Times article on the topic:
All that being said, when we return to the question of the genetically engineered salmon, Rabbi Menachem Genack, the chief executive of the Orthodox Union’s Kosher Division, believes that the genetically engineered salmon would probably be kosher even if some of its genetic material came from trayf. “If this is a salmon that has fins and easily removable scales,” Rabbi Genack told me, “that is what’s critical.”