That looks to me like an old (obsolete, discontinued), proprietary phone system. Just a guess, but it probably uses some sort of digital communications over those phone cords, not standard analog telephone signals. These were popular in hotels some years ago, one reason being that the phones were useless if stolen. Is this some sort of senior/assisted living community with a centralized phone system?
Hopefully, you didn't fry your OBi equipment from plugging it into that system. Just because it has the same shape and size jacks doesn't mean it it is POTS (Plain Old Telephone Service). And, by the way, the term is PSTN, for Public Switched Telephone Network, not PTSN.
