What are the criteria that determine if a research group/professor is actively pursuing research?
You have a piece of evidence that doesn't tell you very much. But there is a simple way to find out what you need to know. Send a message to the group's PI and express your interest in that area and ask whether they are still doing research in it. Is there any, more recent, work that they can share with you? Are there students in the group with whom you might correspond. 

It could be anything from "we have ten papers in the pipeline" to "we dropped that a few years ago". Or maybe even "we think we are on the brink of a major breakthrough and have been quiet about our work while we refine it." 

But only they know the real situation. Maybe they will be able to honestly share enough to let you know whether to move on or pursue it. 

I'll note, also, that the lack of publicly visible productivity doesn't necessarily equate with a lack of productivity altogether. Research breakthroughs can't be scheduled. If they could be, then it wouldn't be research. 

Note that according to Wikipedia, Andrew Wiles worked almost entirely in secret for six years before coming up with a proof of Fermat's last Theorem. There were a few glitches initially, but he was Knighted for his breakthrough.