Yes, you're right, I totally missed them. Those look like USR 'Courier' modems but the resolution is really crappy so hard to be sure and it looks like there are multiple types. There might still be modems in the boxes themselves as well. It doesn't look like more than two modems per box if there isn't.
yes, most of them look like USRobotics Courier modems. Note that not all the machines have one, and some have two.
Assuming that the parent commenter is right and that they are using internal line cards, I wonder if the external modems were being added to support higher speeds.
However, the fact that we can see at least 2 (but I think four) 66 blocks means they had 50 to 100 phone lines for the machines visible, which would make sense that the external modems are the primary connection and no internal modems are being used, based on the number of modems visible and the fact that each 66 block can handle 25 lines.
I think you're right and that there were only two modems connected to the boxes so that's just the built in serial ports, here is another copy of the same picture by someone that apparently funded the board with some details:
This almost confirms it then, each machine has an external modem tied to 1 phone line per modem, and there are no internal modems in use. The picture shows 50 modems that I can see, and the original article indicates that it's around half of their total setup. Scott notes that they had a T3 (likely a frac T3) with 140 dial-in nodes, which aligns with the articles guess of 134 machines.
So I would say that almost definitely, they are using 1 (or 2 for some on the right side of the photo) external modem per PC connected to the 66 block, those analog phone blocks tied back to the channel bank/multiplexer, and the carrier's T3 tied in there.
No internal modems used at all.
And the person who posted the photo on twitter is none other than Scott Miller, founder of Apogee Software, publisher of some of the most revolutionary games of the late 80's and early 90's, and this BBS (Software Creations) was the cornerstone of distributing the shareware versions of those games. Very cool bit of history, I remember dialing in to Software Creations to download Commander Keen!