Originally, an "internet" was a network which linked together other smaller networks, for example two university campuses which each had their own, incompatible

Originally, an "internet" was a network which linked together other smaller networks, for example two university campuses which each had their own, incompatible, in-campus networking technologies. You might have University U1 running IBM and University U2 running Decnet. IP protocols had nothing to do with it. From there, we got the later backformation "intranet" for a network within an organisation. When the TCP/IP suite became ubiquitous, some people concluded the distinction between "the" Internet, as defined by the root DNS servers, and "the internet" was superfluous, as there was essentially only one internet. There are no doubt internets running factories that are not "the internet" but for practical purposes the term is not ambiguous, as one would normally mention if such a network was disconnected. The article is wrong in its definition of lower-case "internet" as an instance of any network running the IP stack. For what it’s worth, the most recent Australian government style guide changed "the Internet" to "the internet". (But it’s not actually published by the government, and this edition has been controversial for other reasons.) I might personally use the upper case version if I thought there might be some ambiguity in the context, which would be almost never.