Someone who reads it will come away with the impression that science proves that Trump has no good arguments.
Only if that person is largely incapable of reading an article that's neither very long nor very complicated. I'm sure there are many such people around, and for all I know there may be a lot of them among Salon's readership, but while I agree that "careless readers may come away with the wrong impression" is a reasonable criticism to make it seems grossly unfair to call the article irrational and bulveristic on those grounds.
the article assumes that Trump's popularity needs to be explained away
No; it assumes that the level of media attention he's getting relative to his support from the GOP establishment needs to be explained (or, if you insist, explained away).
which in turn assumes that his positions are bad
No, not even if we suppose that (contrary to my claim above) the article is assuming that Trump's popularity needs to be explained away; what it would then be assuming is not that his positions are bad but that they're unpopular, or at least would be without Trump's alleged skill in manipulating emotions.
but does not offer actual arguments against them
Because assessing the quality of Trump's positions is no part of the purpose of the article.
is written as though it assumes
I don't see that it is. I would expect an article that actually assumes that to say different things.
As part of my broader project of promoting rationality to a wide audience , I published an article in Salon entitled "Get Donald Trump out of my brain: The neuroscience that explains why he’s running away with the GOP." I'd welcome your thoughts on this article itself, and also meta-comments on the strategy of using mindkillers such as politics to raise the sanity waterline by smuggling in rationality memes into such popular and populist venues.