My first "real internet connection" (not prodigy or compuserve or local BBS) was connecting to the county library's gopher server via modem (Likely with QModem), navigating out to other gopher servers and then being able to telnet from there.

I'm reading it as they used the IBM AT as a serial terminal, running QMODEM as the terminal emulator, for a Linux host that was connected to the Internet via modem.

The clue is in the rs232 mentioned in my comment. Linux is a Unix, even if nobody does it today you can configure an external terminal via serial port and use the system as if you were a user.

The two Linux box were one with the modem and the other via Nat (Ethernet but with old coaxial cables). The AT was just a terminal.

qmodem probably makes a perfectly good terminal program. So presumably the 3rd PC gets its internet connection (so to speak) by being a terminal for one of the other 2.

Modems were the way to connect to the internet providers so I guess he used QMODEM to dial up.