Is the player a woodcutter?
The idea that the protagonist cut down trees and the forest is taking revenge is a fan theory. The developer explicitly identifies that explanation as fan speculation.
Do not treat that theory as the game’s confirmed backstory, even when it is repeated in videos or comments.
What has the developer said?
When asked why the trees hate people and who gave them awareness, the developer said they would try to hide interesting secrets, but felt that too much official explanation would take away from the experience.
What is the official explanation?
There is room for interpretation, but no specific cause to present as the official solution. That also does not mean the full game can never add more story or secrets.
For the demo’s unusual arcade behavior, see arcade and high scores.