“... n that granted freedom to any rebel-owned slave who would take up arms for the King.”
REBEL-OWNED. Again, it did not abolish slavery generally.
That’s from Dunmore’s. Dunmore’s required slaves to take up arms with the Loyal government.
Philipsburg doesn’t. It was a general emancipation. And like Lincoln’s it was issued as a war measure.
Neither emancipation was the causus belli. Both wars were intended to put down rebellions that were seeking independence.