I've had dogs communicate with me by angrily running towards me and barking. This conveyed danger and told me to get out of the way.
I've once had a small avalanche do the same as well.
People would call me looney though if I told them that the mountains communicate with me, and I listen.
The mountain communicated nothing to you.
If you were hunted and killed by a mountain lion, it would be akin to the avalanche. It did not intend to send you any message, even if you managed to spot it before it attacked you.
The dog fully intended for you to know.
You define it as requiring intent. Fair.
I can formulate just as valid of a definition of communication without intent. The way you dress communicates certain things about you, whether you intend to do so or not. My pheromones communicate a lot of things about me, even though I don't intend them to do so.
Again, it's not so simple unless you use a single narrow definition and forcefully ignore all other ones (some of which are easier to accept than others).
Do you know of Alex the grey parrot? It seems to be the only animal that we have recorded actually asking questions: