It looks like the area gets a lot of water
(from showers? from overflowing toilet?).
It also appears there is a door there, possibly separating that cabin
from the salon
If so, you could use a different type of sole/floor covering in that limited area (assuming it is in an enclosed cabin).
Gluing down rotting wood
does not seem like a good idea to me.
And it looks like the area gets wet. I would first consider how to reduce water
in that area. If the head
is a "wet" shower
, it may get wet frequently.
I would consider taking out the wood
there on the sole and replacing it with synthetic "Plasteak" type floor covering or something similar that is not affected by water (will not rot).
This free video on youtube gives step by step instructions on how to use Plasteak on a boat
. It made a very nice improvement to an older boat
NOTE: I am not suggesting that someone take up all their sole to swap it with Plasteak. But, I am pointing out that there are rot-free alternatives to sole/floor covering materials that do look "nautical" and nice.