After a little looking, I figured out that company calculating the J-Score™ does not obtain the data from Stack Overflow directly:
Joberate leverages only publicly available Social Data in calculating a person’s J-Score™, which means that there is
no violation of anybody’s data privacy. Social Data is legally licensed from Social Media data resellers (i.e. GNIP,
www.gnip.com) and otherwise obtained using Joberate’s patent-pending platform, which measures the intensity of a
person’s job seeking activities, taking into consideration time, volume, and relevance when calculating a person’s J-score™.
Source
If you look at Gnip's page here, they list Stack Overflow. Gnip uses the Stack Exchange API, so I will assume all the Stack Exchange data was gathered by Gnip via the API.
You can get questions and answers from the API. Due to the license (CC by-SA), you will also get the username and profile image associated with the post.
At first, I couldn't figure out what value post data has to Joberate. But I found a possibility:
In addition to J-Score, the platform performs psychological profiling based on the NLP (Natural Language Processing) of CV’s and Social Data.
Automate matching the ideal candidates based on company culture, candidate’s job seeking behavior, preferred communication style, and their availability.
Clearly there's some merit to this. It benefits everyone when it's a good fit; you don't want to realize you hate your job/company after you've invested time.
Legality
Let's look at some selections from our Terms of Service:
[N]o Profile Content, including API Profile Content, may be used in any way that implies a user is affiliated with, has signed up for, or is in any way associated with a third party without explicit permission from Stack Exchange or the user.
Under no circumstances will Subscriber use the Network or the Service to
(a) send unsolicited e-mails, bulk mail, spam or other materials to users of the Network or any other individual,
(b) harass, threaten, stalk or abuse any person or party, including other users of the Network...
(e) copy, download, or scrape any Personal Profile Content for the purpose of indexing software engineers, social recruiting, sourcing, employment-related services, compiling databases of employment solicitation targets, providing content for a hiring platform without the express permission of Stack Exchange or the User.
Here's my look on this.
That first section may or may not apply here. The software appears to only produce the score. A higher J-Score indicates that you may be looking to leave but it's not clear how Stack Exchange data fits into this. Without more details, as Tim Post says, it's hard to tell what they do with the data (besides machine learning), or how it goes into the score.
You might get emailed if you're using Joberate's system, but that is not bulk mail or unsolicited. Section (a) does not apply.
Section (b) might have something. Of course, without being contacted, you cannot be harassed or threatened, but stalking seems to fit. Unfortunately, I think that the legal definition may be a bit different:
Although stalking is illegal in most areas of the world, some of the actions that can contribute to stalking can be legal, such as gathering information, calling someone on the phone, sending gifts, emailing or instant messaging. They become illegal when they breach the legal definition of harassment e.g. an action such as sending a text is not usually illegal, but is illegal when frequently repeated to an unwilling recipient.
The Violence Against Women Act of 2005, amending a United States statute, 108 Stat. 1902 et seq, defined stalking as "engaging in a course of conduct directed at a specific person that would cause a reasonable person to—
(A) fear for his or her safety or the safety of others;
(B) suffer substantial emotional distress."
From Wikipedia
From that section, it's pretty clear that stalking legally refers to repeated harassment. "Information gathering" isn't illegal on its own, it would seem.
Sections (c) and (d) are excluded from my quote as I did not feel that impersonation or posting wrong information respectively were relevant here.
Section (e) also looks like it might have something. That is, until you remember that "Personal Profile Content" refers to:
Profile Content that is NOT available via the Stack Exchange API