I am in the process of adding a bathroom in an "alcove" area off a bedroom. The floor appears solid, but is some kind of a pressed wood. Will be an appropriate material to support a toilet and tub or should I use something different? I anticipate covering it with vinyl flooring.

The pressed wood is probably the sub floor and you can put pretty much whatever you want over a sub floor. I put vinyl over a couple of subfloors.
It should all be fine I would think

Pressed wood will be just fine. Back in the 70's I installed plumbing in mobile homes. All had pressed wood floors. Good luck, tom