Octane rating CAN absolutely has something to do with power IF tuned to take advantage of it.
In the context of this thread, a boat using an OEM ECM, there is no power benefit to running a higher then recommended octane.

Now, in the custom world, there is a benefit to using higher octane. But in reality, the BTU from different pump octanes is about all the same. The benefit comes from the proper ignition point, as the higher octane resists self-ignition due to the added heat of a higher compression engine.