I am installing solid iron gates at a home a few hundred feet from a (brakish water) river in Florida.

I had the gates powder coated and requested a satin or (at the most) a semi-gloss finish of about 15% to 30% gloss.

Instead, the power coater did the gates in a high gloss. He claims that it is better protection (for the metal) and will last longer. He also claims that the sun and salt will dull the high gloss in a matter of a few months.

Two questions:

Is it advisable to use a higher gloss to protect the iron from bright sun (12 months/year) an brakish water spray and humidity?

Will the finish dull and soften, and if yes, how long does it take?

The high gloss should dull a bit. Don't know how long under your conditions. Ask the guy if there is a way it can be softened.

I used to help out friend who owned a dirt modified race car. He had his frame of the car powder coated a high gloss and after a few races the gloss dulled. This of course is from constantly getting dirty. We did wash the car after every race.
That was the main reason he got the high gloss coat.

Actually the issue is you asked for a specific type of coating and the company did not provide you the serive you asked for, but changed it without asking.

I would personally demand that they re-do it, the way you want it done,
If for no other reason than to teach them a lesson that they can not change a customers order without asking him.

You might better leave well enough alone. If it was an epoxy, it will quickly lose its gloss in your Florida sunshine. Just recoating it would leave an excessively thick coating more prone to chipping. I wouldn't trust them to go through what stripping it might take.

Epoxies are frequently the material of choice for powder coating. There is a good reason why the automotive companies don't use epoxies for the top coat, they dull quickly. I can't say how soon.