This would suggest, perhaps smart medicines capable of changing their active makeup based on logic in response to the actual conditions in the body.
Heck, given a lot of advancement it isn't that terribly outlandish to imagine simple turing complete computers capable of outputting different dna or even proteins. If that were possible, the benefits should be obvious. Of course, that's a rather large extrapolation from the limited results in the article.
* Self-inactivating medicine. For example, insulin that stops working after blood glucose levels return to normal, so that insulin shock does not occur. Also, one could make a medicine that automatically inactivates if its own concentration goes too high, thus preventing overdose. Quicker inactivation can also limit the opportunity for side-effects.
* More precise targeting. One could custom design a medicine such that ot only becomes active at the desired site. For example, an antiviral drug that only activates in areas with high concentrations of virus. Again, this would help limit side-effects.
As I understand it, plenty of research happens with no clear goal in mind, and plenty of research winds up good for something other than the original goal. See the Post-it note. This is, in my opinion, because you can't fully understand the technology until it actually exists!
Looking over the paper, it looks like they figured out how to combine their seesaw gates and thresholding gates into AND and OR gates, then from there, used dual-rail asynchronous logic to make a four-bit square root calculator. They can't make NOT gates (or NAND, or NOR), so each bit gets two "wires", holding opposite values; this lets them make arbitrary logic without NOT operations.
There's a pretty slick simulator program you can play with here, along with more information, if anybody's interested: