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Usually after a fight with a big fish, the fish is (obviosuly) exhausted. In lakes and rivers, its easy to hold the fish in the water until its recovered and then let it swim off. Might be more difficult to do that with something that size on a boat. Chances are it'll have been fine though...
The Orkney Skate Trust have had recapture of an 82lb tagged skate, recaptured the next day, so that indicates survival is perfectly possible and the skate was able to make the same mistake again so certainly hadn't been put off its food.
I have been on a boat when a 230lb skate was caught, it was pretty quick to tag it and get it back in and it swam off powerfully. Not sure how long this chap has his out for and it it appears to have been gaffed, though in the wing, so shouldn't cause any lasting damage.