You can think of wave as the process of transmitting energy through a medium, this is perfectly fine. Or, you can think of the wave as a manifestation of the energy being transmitted. These may just be different ways of defining the wave. However, I think the definition I used is more conventional, as for example we normally think of water waves on an ocean as a physical thing, rather than a process. Interesting perspective though and thanks for your bringing this up @brainkerr !