According to John Kay, the Shang were one polity of many in that day. They weren’t a unified state yet, they were a collection of allied settlements bound by family ties and ritual. There were other settlements of different communities interspersed with Shang sites, perhaps similar to how 5th century Britain was spotted with ex-Roman, Anglo-Saxon, and Norse villages.

But Kay also says Chinese writing today traces back to the Shang writing system, as well as some other cultural elements such as bronze working. So they were especially influential, if arguably not quite “Chinese” yet.