As far as I know, there is no automated service to do this. One of the reasons is that mass download of research papers is frowned upon by the publishers (look up the sad story of Aaron Swartz, for instance).
If you want to build an automated (or semi-automated) solution yourself, one of the trickiest steps is identifying correctly the cited papers from the citation strings. For this you can use a research paper database, such as Scopus, Web of Science, or Pubmed. For instance, Scopus displays the references of a given paper in its page, and for each paper you get a "view at publisher" link that redirects you to the article page on the publisher website. This web page usually has a "download pdf" link inside it (usually paywalled, too), and since most papers come from the same major publishers it is should be possible to scrape this link automatically at least for these publishers.
Unfortunately the paper that you link to does not seem to be indexed neither in Scopus nor in Web of Science --- maybe because Hindawi is not one of these most "mainstream" publishers. It is in Pubmed, though. I am less familiar with it, but if you click on the references you also get a page with a "full text" link in it.
Note that Google Scholar does not display "forward" citation information, instead; only the reverse (papers citing a certain paper).
As mentioned in the other answers, you may be violating some terms of service if you do so. Terms of service are not the law, though, and I think you can only get into a very limited amount of trouble for that.
A Google search returns a few tools to do similar things:
I do not have experience with any of them, though, and I don't know if they are mature/stable enough for casual use.