Definition 1.1: "Money paid as part of a special transaction, for example for a privilege or for admission to something." I'd say that applies.

Those literally were indeed fees.

The National Science Foundation paid Network Solutions a payment, per registered domain, in exchange for the service of registering it.

IP-Addresses and domain-names are only tangentially related. Just because you pay a fee per domain-name does not mean it's the same for network addresses.

My comment is addressed at "Same goes for DNS. You used to request the name and it was yours. No yearly fees."

> Originally a file named HOSTS.TXT was manually maintained and made available via file sharing by Stanford Research Institute for the ARPANET membership, containing the hostnames and address of hosts as contributed for inclusion by member organizations.

https://en.m.wikipedia.org/wiki/Hosts_(file)

And where do you think the money to pay the ARPANET contracts came from?

Well, in case anyone was wondering, the answer is US taxpayers: http://www.columbia.edu/~rh120/ch106.x07

Sorry. Didn't catch the context.