There is probably a "brick" plugged into a wall outlet (even though it might be hidden in the electrical cabinet) like used on laptops that converts AC to low voltage and rectifies it. I will bet it will also run fine on 12v DC straight from the boat's batteries.
When I replaced my old (well 2006 wasn't so old) analogue TV with a wide aspect digital one, I went to Best Buy and looked at TVs. I followed the power cord down to where it plugged into a terminal strip. If it was a brick, I unplugged it and looked on the back. Some were 19V like laptops, but I finally found one that was 12V.
So I took it home, clipped off the leads to the brick and wired those leads to a spare DC breaker on the main panel. Worked great.
I am not sure if a 19V TV wouldn't have worked just as well.