Just had a quick look at
https://www.clawhammersupply.com/blogs/moonshine-still-blog/home-brew-recipe-new-england-ipa-neipa
If this is what you mean, then the first hop addition doesn't go in at the end of the boil. They specify "first wort" hopping with a hop I've never heard of - Azacca. I don't do first-wort hopping, but as far as I'm aware it means putting the hops into the boiling vessel, then sparging the mash onto them (or just pouring in the decoction if you don't sparge). The hops are therefore in the boiler as it warms up, not just put in for the boil, and are left in for the whole boil. Apparently, this can make a difference - sounds unlikely to me, but maybe it does.
The 60min boil would have extracted a lot of bitterness from the first-wort hop. I've just looked up Azacca, and it is very high alpha-acid (AA) indeed at 14-16%. not precisely sure what 0.75oz means, but I'd guess at about 20g, so that's a fair amount of bitterness. You won't have got anywhere near this if you didn't boil the hops. But..... The recipe then has a lot of hops going in after the boil. Again, all the units are foreign to me, but it looks like over 100g of pretty high AA hops. They chilled the wort, you didn't. So, you'll have got a hell of a lot more bitterness out of these hops than they did.
Would your extra bitterness from the steeping/post-boil hops make up for the lack of bitterness from the boiled hops? Almost certainly yes. Possibly, they'd impart a hell of a lot more, so your beer may be very bitter indeed. A dark art this - estimating hop isomersiation (i.e. the development of bitterness) in a slowly cooling wort over a lengthy timespan. Best way around this - don't do it! Don't put a load of high AA hops in the kettle at flameout and let it cool naturally. If the recipe says that they chill to 150°F, then wait until your wort has naturally cooled to 150°F (whatever that is - sounds about mashing temperature to me so maybe in the 60s C) and then add your hops. At this sort of temperature you can leave them in for ages. Flavour will be extracted, but the beer won't get much more bitter. And, yes, you might as well remove the hops before fermenting. Nothing to be gained by leaving them in the wort.
As for the dry hopping, I assume that the 2-stage dry hopping is because they've used a shed-load of hops and didn't want them all in the beer at once because of the volume. Not something I've come across before, but I can see no point in it if not for this reason, and even then only if you are using whole hops and not pellets. The recipe does state: add the first dry hops in a bag, then remove them and add the second lot. I'd then leave the second lot in until fermentation had stopped completely.
Oh, and the dry hops will contribute zero to the bitterness.