There's no formal government approval of higher education in the U.S., but there's a quasi-official system of accreditation that effectively puts a stamp of approval on some programs. It's still legal to offer unaccredited programs, but they aren't eligible for some kinds of funding, and some kinds of legal recognition might also be tied to that status (varies by field). My guess is that they are not seeking accreditation, since they don't seem to be aiming to provide something similar to a traditional university curriculum. In that case, the space is basically unregulated. Some details: https://en.wikipedia.org/wiki/Higher_education_accreditation...
An online-only school can be accredited at least since the '90s, though, in cases where it does seek to provide education equivalent to a traditional physical-classrooms university, and wants equal recognition. I believe the first online-only university in the U.S. to receive accreditation was Western Governors University (founded 1997): https://en.wikipedia.org/wiki/Western_Governors_University. They charge about $5500/yr, fwiw.
An online-only school can be accredited at least since the '90s, though, in cases where it does seek to provide education equivalent to a traditional physical-classrooms university, and wants equal recognition. I believe the first online-only university in the U.S. to receive accreditation was Western Governors University (founded 1997): https://en.wikipedia.org/wiki/Western_Governors_University. They charge about $5500/yr, fwiw.