Yes, they are on the Official List of companies on this site. I suspect somebody had a reason to put them on it.
Over the years I have learned that some companies do only mystery shopping while others include mystery shopping as one item in a large menu of services to their clients. You have heard of Market Force and Harland Clark perhaps? Each is notable to mystery shoppers. However each also provides many additional related services to their clients. If you Google the client website for each you can see the details. As shoppers we often have no reason to be aware of those other services, so we therefore think that mystery shopping is all they do.
Turning to Hope Research, I haven't encountered them or researched them before. However, it is possible their business is thriving, but with so little mystery shopping that they get so little attention on this board.
As a signed up shopper, you could check the job board for shops in different areas. You could ask them directly where they shop. You could also Google the company for their main website or other information. Maybe someone else will give us some details about their mystery shopping. The thing with this business is that you never know when companies offer new shops from new clients.
Good luck.
Happily shopping Rhode Island and nearby Massachusetts and Connecticut