It is unfortunate that the NYT is confusing 5G, which is a certain version (15?) of the LTE advanced specification, with the use of millimeter wave frequencies. Here in the U.S. at least one major carrier is deploying 5G on frequencies below 1 GHz.
As someone who currently works in wireless comms I think we can say "5G" is a pretty meaningless term. I presume, as you suggest, it originally referred to the new LTE but honestly the definition "literally any wireless tech created between about 2015 and about 2020" seems to be universally accepted!