The protests themselves are not "spying" per se but rather a tactic used to promote pro-Chinese government propaganda. According to the linked article, members of the student group have been accused of spying.

Straight out of that article:

Li Fengzhi, a longtime employee of the Chinese Ministry of State Security who came to the United States in 2003 as a graduate student at the University of Denver, said that the Chinese government did not see the group so much as a spying operation, but rather as a propaganda and “information collection organization.” Mr. Li eventually defected and was debriefed by F.B.I. counterintelligence agents about the group’s activities.

> Li Fengzhi, a longtime employee of the Chinese Ministry of State Security who came to the United States in 2003 as a graduate student at the University of Denver, said that the Chinese government did not see the group so much as a spying operation, but rather as a propaganda and “information collection organization.”

I could not find any other sources to cross-reference this information. All the information that I could find about Li Fengzhi (wikileaks, washingtonpost) talks about his link to Ministry of State Security (MSS), and make no mentions of comments made on the student groups. So it would appear that he was talking about MSS when talking about "the group".

- http://www.washingtontimes.com/news/2009/mar/19/exclusive-ch...

- http://voices.washingtonpost.com/spy-talk/2010/09/li_fengzhi...

- http://voices.washingtonpost.com/spy-talk/2010/10/li_fengzhi...

- https://wikileaks.org/gifiles/docs/12/1231001_re-spytalk-li-...

Of course I could be wrong and NYT had the first hand information on that, but the entire Li Fengzhi story ended in 2010 so it is not likely that NYT had the information without publishing it before 2017.