I just watched "Arena" to check. And... the damage to continuity isn't that bad, imho.
The Enterprise is sent a message to come to an outpost world, where the crew could be given some shore leave. When they arrive, they find a world that's been decimated by an attack. There are aliens still on the world, and they bombard the away team. The team never sees the aliens.
The crew of the Enterprise in orbit explicitly don't get in range of the Gorn ship for visual contact. What they get off of sensors, they don't recognize. That's entirely fine - between SNW and TOS, the Gorn develop new ships that don't look like their old one on long-range sensors. This is a non-issue.
After Kirk blows up the aliens on the ground, the aliens ship takes off. Questioning a survivor, Kirk discovers that the outpost never sent an invitation. Kirk recognizes that the aliens must have lured them to the planet. He muses on why, and comes to the answer that the Enterprise is the only Federation ship in the area, and this is prelude to invasion!
(In retrospect, Kirk is being dumb here - or, more accurately, the writers are being dumb, because they needed to fabricate a reason for the Enterprise to be here. If the aliens know there's only one ship in the area, there's no need to lure the Enterprise in - an invasion fleet would paste the one ship anyway. We, with SNW, can surmise that the Gorn lure the Enterprise in because they freakin' HATE the Enterprise.)
Kirk gives chase to the alien ship, and eventually both the Enterprise and the aliens are caught by the Metrons, who set up the Arena thing. And this is where the first (and pretty much only) canon violation happens.
The Metrons use the word, "Gorn," and Uhura, Scotty, and Spock, who are on the Bridge at the time with Kirk, do not immediately go, "Oh, crap, Jim, we know these guys, we are in deep kimchee!"
Kirk is then whisked away to fight the Gorn Captain. Kirk has not (so far, iirc) been part of the SNW Gorn episodes, but it is hard to believe that Sam Kirk wouldn't have mentioned them, unless the Gorn become classified. So his ignorance is a bit of an issue. But it doesn't really change the plot of the episode.
Yeah, but "launch an interstellar offensive and notify alien governments to stay the heck out of the way" is not an instinctive response.
I have a current No-Prize explanation for the Gorn behavior, until they give me one. The basic answer is in one term: Life stages.
I surmise that the majority of the Gorn we have seen are young, non- or barely-sentient. It is this stage in which they are extremely competitive, violent, and weirdly, breed. The young stage are the ones who are so strongly bound by instinctual responses.
The Gorn Captain we see in TOS, and maybe the one we saw in the spacesuit, are mature specimens, possibly past breeding age, sentient, and no longer so strongly bound by instinct. These mature specimens are the ones who maintain Gorn culture, build ships, and so on. They are brutal, but can make plans and choose to act to avoid full-scale wars and such.
So to explain the finale - There's a coronal mass ejection where Scotty was. That sends the young Gorn into a frenzy. The mature Gorn say, "Well, our kids are going to consume each other unless we give them a target," so they drop them off on the colony world and let them hash it out. They message the Federation to stay the heck out of the way, because a full-scale conflict isn't something the adults want at this time, and they don't want the Federation to figure out their behavioral patterns like this, lest it be exploited.
At the colony, we see a couple of young Gorn choose to not attack humans. This one has already fed and bred and matured to the point where it isn't entirely driven by instinct. It is on its way to becoming a mature, sentient individual. I don't know any other reason for that scene except to telegraph that there are changes as Gorn mature.