The premise seems to be:
1. There is a gene associated with a brain pathway responding to the smell.
2. The more this gene is expressed, the more the stronger the pathway.
3. Brain functions that depend on this pathway have a feedback mechanism that result in hypomethylation of the gene in at least sperm cells (egg cells weren't mentioned). This increases expression in the descendants. From what I understand, hypo methylation does not entail any alteration of base pair sequences.
4. As the parent post mentioned, this doesn't mean passing on aversion/affinity, but potentially increased sensitivity which may aid in speed of learning these traits.
That's based on my reading of the abstract. The abstract didn't mention any kind of known or discovered chemical signal for the brain activity to result in the hypomethylation in the sperm. My question would be if anything else in the experimental protocol could have triggered this in a manner not directly caused by the brain activity. My next question would be if this work can be reproduced with a different chemical pathway.