LOL! Someone finally noticed/asked about that piece of wood!
This is the house that idiots built/updated.
When the area above the range was originally built/updated, that piece was used to hold the "top" of the area up. There is a 3/4 board behind the face holding the soffit and left side of the cabinet in place. It's hard to describe how it's all put together. It wasn't originally a cabinet, just some shelves.
In order to remove the piece on the right side, we would have had to take down the soffitt that goes to the ceiling.
There isn't even a way to cut the piece down to hide it behind the face frame, so when the doors are up, it will be hidden by the door.
It was originally hidden by a 1 x 6 on the face of the area. We cut the 1 x 6 down to match the existing cabinet next to the stove.