It's another entry in the DMC franchise. Sequels do not have to share continuity (e.g. Final Fantasy), they can simply he the continuation of a franchise. I suspect DmC's existence as a reboot is part of the reason Capcom stated that DMC5 is a direct sequel to DMC4 rather than just stating that it's a sequel. It clarifies that it's both in the same continuity as DMC4 and a continuation of DMC4's story.
That said, it's a redundant and confusing descriptor the way I used it. Still, it differentiates it from a spin-off entry in the series, as DmC was intended as the new direction for the series at the time.