Nope, no real principles from submarine engines translate to space. Nuclear "Engines" on Submarines are not actually nuclear engines at all. They are steam engines.
The way they work, is the submarine has a nuclear reactor that makes water hot. That is all the nuclear reactor does, it takes cold water and makes it hot enough to turn to vapor. That steam is then fed into steam turbines, which use the pressure generated to turn a mechanical drive that is connected to the submarines propellers. The Submarine moves through the water with the propeller. The steam turbines also power generators that provide all the electrical power for the submarine for stuff like life support and steering. Now you can actually hook this system up to any form of mechanical propulsion you want, as long as you can drive it by turning a shaft. Wheels? Tracks? Hydrojets? All perfectly fine, just hook them to the drive shaft.
However none of those work in space. You could still run a nuclear reactor, but it would be a bad idea, because it is basically impossible to vent heat as fast as the reactor produces it. In a normal steam turbine you want the water to cool down, then cycle it back into the reactor to heat again. In space, there really isn't anywhere for that heat to go, once something gets hot it kind of just stays hot for a very long time. Second problem is that there is nothing really that can make you move by just turning a drive shaft. All of those forms of movement require something to push against to move the vehicle forward, it can push against water, air, or the ground, but it can't push against nothing.
So any form of nuclear engine on a space ship has to use a fundamentally different principle. The one being discussed here basically focuses the heat on a small amount of Hydrogen, and then shoots that hydrogen at the speed of Plaid. Which makes the vehicle go in the opposite direction of the junk of hydrogen you just yeeted into the cosmos. Basically it is traveling by shooting a radioactive gun in one direction so the recoil knocks you in the direction you want to go. You need fuel to run the reactor, and "Ammo" to keep shooting until you get to the desired speed (And you need the same amount of ammo if you ever want to slow down again)