Odd, but yes, you've nailed it. His jacked up nutritionally superior sperm (not his DNA) encourage her as yet un-ripe eggs to develop better than ordinary run-of-the-mill sperm would. It makes sense evolutionarily speaking because in a normal mating scenario, he would be the one reaping the rewards of that, in that he would be able to stick around and fertilise those eggs. The manipulation in the experiment prevents this of course, and instead hands her (and her lovely eggs) over to a male who has been lacking nutrition.From the link: "molecules in the seminal fluid of the first mate being absorbed by the female's immature eggs and then influencing the growth of offspring of a subsequent mate." So those molecules aren't DNA, but some other factor? So the superior diet of the first mate affects his sperm some days or months later, causing it to have some kind of growth factor in offspring (which offspring are not his own) of his female mate, again, some days or months later? The well fed fly's sperm actually somehow nutrifies his mating partner's eggs? Odd.
His sperm doesn't elicit large larvae, no, but it's still more than capable of fertilising that egg. There's nothing wrong with his DNA, so fly babies ensue. If the under fed fly is the one mating first, his sperm doesn't trigger her eggs to strongly develop, so even when the over-fed fly is the one to impregnate her on that cycle, the babies resemble the weaker fly in stature. This is additional evidence that whatever is going on here, it is not the DNA in the sperm that is responsible.Therefore if a female fly mates with an underfed male fly, his sperm will have no effect on her immature eggs.
Here's a super simplified explanation of what the study shows in each of it's conditions. Note that since flies don't differ much in features, but do in relative size, that's why the authors are making the claim that they physically resemble the previous donor. They are bigger or smaller than the genetic father. Which as you say, can be due to things like better diets, and apparently also this protein-transfer mechanism with the sperm.
under fed fly > regular eggs + well fed fly DNA = regular fly babies (don't look like dad)
well fed fly > super-charged eggs + under fed fly DNA = super-charged babies (don't look like dad)
under fed fly > regular eggs + under fed fly DNA = regular fly babies (look like dad)
well fed fly > super-charged eggs + well fed fly DNA = super-charge babies (look like dad)
But at any rate, there is no DNA transmission, as per the OP's assertion. So it's all moot.
Yup. Pretty much!