What is eating this tree?
Your ornamental cherry tree is having major troubles that likely started long ago.
The large limb in the middle is dead, and while there could be insects in there that naturally break down dead wood, they are not eating or killing your tree.
The dead wood being thrown around is likely from a woodpecker or other bird feeding on insects or more likely, excavating a nest cavity.
We can't tell from your photo how big this tree is or how close to your swingset it is, but that branch is not structurally sound and will likely fall soon. If it's fall would threaten people or property, we'd have it removed soon. If not, it can be left for wildlife.
In looking closer at your photos, the shelf-like fungal growths on the right branch suggest that is dying as well. On the left side, the partial dead branch attached to an open cavity suggests rot in the trunk overall.
Here is our publication about when to remove a tree: http://extension.umd.edu/hgic/plants/how-do-you-decide-when-remove-tree