I used to work in this industry.
US universities are generally open to making money through course offerings, certificates, and other ventures that leverage their brand and network while not jeopardizing their reputation and their accreditation. For many universities below the very top-tier, finding ways to make money is a matter of survival.
Harvard is obviously one of the most famous brands, and they're also one of the best at pursuing profit-making ventures by any means.
"Who runs these programs?" is an excellent question! I don't know about HBS Online in particular, but generally, universities farm out their certificates and even some degrees to Online Program Managers, aka OPMs.
The most famous OPM is 2U. Check out the LA Times reporting on 2U's deal with USC. Coincidentally, a few years ago 2U paid $800 million to acquire edX, a non-profit started and run by Harvard and MIT. Curiously, 2U's stock (TWOU) is down by 99.5% over the past five years. It's complicated.