[bravura]

you're incorrect. To be more pedantic, sequence labeling is a special case of parsing. Parsing need not be hierarchical. Chunking, aka shallow parsing, is a sequence labeling task.

Parsing is commonly understood to infer an hierarchical structure, but that's not required.

Indeed, the Latin root leads us to understand that parsing is about breaking an object into parts. That these parts nest according to a particular grammar is something of an important implementation detail.