Sailors are often pedantic when it comes to terminology so it's helpful for me to learn the correct terminology and so I can be specific about which sail I'm speaking of. It is probably accurate to call it "A sail", "A stay sail", "A Daisy staysail" in increasing order of specificity. I don't know the reason for the OP's post... perhaps it was a quiz? perhaps he's pedantic like me? perhaps he's just curious.
You're right though, it probably isn't making much difference in that photo as they're usually used in light winds I would think. In the cases where I've used a Daisy, it made a "huge" difference in relative boat speed; I know that doesn't seem like much in the grand scheme of things but every little bit helps in a race. I think it is probably hindering, not helping the fellow in the photo above.
(Another use for a spinnaker staysail is to keep the crew busy on light air days so they don't get bored...)