Earlier quoted context omitted.
To me it looks like the article is largely told from the perspective of ISPs connecting themselves between each other, and how the constant analog/digital conversions between carriers were causing problems sustaining the 56k data rate that the (analog) last mile was always capable of... and how converting their internal systems and backhauls to digital solved that issue.
Exactly. More specifically, Internet servers in data centers connected themselves to the IP network, not the phone network (not surprisingly), so they almost always had an uplink significantly faster than 56 Kb/s. And the analog local loop had encodings that could transmit at 56 Kb/s. But these encodings were not compatible with the analog-digital conversion used in phone network backbone. While today you'd probably…
The phone companies had enormous sway over the development of these longer haul protocols. The debate around packet sizing almost always favoured smaller cells (especially ATM), which was more ideal for voice - with the added overhead for more standard IP packets. They were also often very connection-oriented, with all the extra equipment overhead required.