Conventional marine engines like Mercruiser, etc. use the reverse of your setup, as I understand it. Usually, the water is sucked out of the source (river in your case) by a raw water pump into the engine. Then a circulating pump, that looks and mounts just like your standard Chevy water pump, circulates that water throughout the engine, before it is expelled out the exhaust system.

Sounds like in this straight inboard application of yours, they bring the water into the exhaust manifolds first, then that heated water is fed into the engine, then overboard. I guess this would work, but what controls the temperature of the water? You are at the mercy of the exhaust manifolds to do this, and I don't understand why they did it this way.

When I lived in California there were a lot of companies doing unorthodox things when building ski boats, so I guess some company figured this is a good way to do it for whatever reason.

If they are still in business, I would get in touch with the manufacturer. Or, you may have something someone has modified for some reason. Sorry I couldn't help, but this system is something I have never seen in my 20 years in the marine business.