This is a tort at minimum; the construction neighbor caused a loss to the neighbor with the tree who's now forced to pay for removal of the tree. So the owner's tree encroached upon the neighbor's property, what rent or fees did the owner pay for that use of said property?
The owner could have controlled the tree's roots keeping them on his property.
As I said sorry for the tree but IMHO subject to an easement the neighbor has the rights to clear his property.
Homeowners' rights have limitations when it comes to nature - groundwater, rainwater, wildlife, trees, etc. Without knowing the local laws, we could speculate for years.
The article is so poorly written.
The picture of the exposed tree roots that grew in a square (likely from a cast iron fence) is pretty funny.