I'm sorry, vinyl flooring in a boat just sounds like something that folks where I grew up would do. Other/better options to replace worn out/ripped up carpeting than vinyl, in my not-so-humble opinion.
New carpet, nonskid gelcoat, and "rhino lining" are three that jump right out at me.
The deck is the usual fiberglass covered plywood. If that's what you want, go for it. Personally, I wouldn't own a boat without it.
My Stingray came from the factory with a "vinyl floor". Its non-skid Nautolex marine decking. When I bought it it was part of their optional "fishing interior" package.
I redid another boat 2 years ago and used Marideck from Cabelas. Once the area was cleaned and any residue from the old carpet was removed, it was a simple matter to trowel on the adhesive and lay down the new material.
Ok, so there is actual "marine rated" product in the vinyl flooring world? Were not talking about going to Home Depot or Lowe's kitchen/bath section and getting that type of flooring? If there truly is a non-skid marine rated vinyl flooring product or two, then okay, add it to my list of appropriate flooring materials to replace carpet.
Never have used it but marine vinyl is availlable and looks very good on the boats that I have seen. The added plus is you just wash off the deck with a hose. When I did my deck I used porch enamel with a packet of non-skid added. Has held up very well for a couple of seasons now and I just use a brush and soap to scrub the dirt and blood out and wash it off.