That doesn't prove anything. Apart from the problems in imaging connections, there's no reason to assume "more brain activation" means better cognitive functioning. Perhaps less is better, since a faster processing leads to a smaller BOLD response. There are more useful statistics in the article: the error rate and the response time. It looks as if "oral" was a bit faster, and had more errors. That might be enough to explain any imaging difference.
Does it mean impaired cognitive function? Well, that would depend on how strong your a prioris are. Is there any reason to assume it does? If not, then this most likely is a chance result. Perhaps oral breathing slightly impaired vision in the scanner or interferes with motor skills. Or perhaps it's the plug in the subjects' noses. This study needs a lot of additional support.