I would personally install the vinyl plank over that riser. The stair nose will need to be glued and it looks like it needs to be installed over the top of the plank. Honestly, it does not look like a good nose to use and I would consider sending it back and looking for a wood nose. You might need to look at another brand to find one.

Have you seen my stair nose video?

Can you share a pic of that nosing sitting on top of a plank. You could probably use the edge of a counter to act as the step. I just want a better visual of this nosing.