the federal census category roughly

In 1910 more than 500,000 black workers, or ten percent of the black workforce, reported themselves to be engaged in “manufacturing and mechanical pursuits,” the federal census category roughly encompassing the entire industrial sector.

I can’t find the flow of the sentence in the bold part. Could someone please help me?

I think it’s a question for grammar geeks which I don’t belong to. The only thing I could observe is that this construction isn’t that rare, especially in written English. Perhaps more familiar look it would have with ‘with’: In 1910 more than 500,000 black workers, or ten percent of the black workforce, reported themselves to be engaged in “manufacturing and mechanical pursuits,”[with] the federal census category roughly encompassing the entire industrial sector.