I never quite understood the term "new media", but we certainly are using it and have to continue to use it. The question is if we need to use it in a "scientific" sense or more in a "political" (not implying that a scientific definition is done in a political vacuum). Having worked in an environment where art historians met "media artists", and works in/of "new media" were exhibited and produced (ZKM Karlsruhe), I came to the perspective that "new media" is a definition after the fact, more a tool for words than a tool for art (maybe that is the prerogative of people not creating the art but creating environments where such art can be supported, produced and exhibited).
"New media" seems to be a label necessary to set it implicitly aside from "old media". Obviously an "ars antiqua" can only be labeled as such, once an "ars nova" has been called out (these terms refer to a muscial period in the early Renaissance in France where exactly this happened).
"Media art" is an even more difficult term - since there is simply no art without medium or media.
And we do have to create and use terminology in order to describe and/or create perspectives of reality. This is most important when one is part of a minority - since the word smiths for the "majority" have "the media" to exert their power.
I have to use "new media" and "media art" in a non-scientific environment, when dealing with people who have power and money to support "new" and who are for whatever reason highly motivated to do so with their power and their money. It is very difficult to convey to them, what I / we are talking about, since they often do not have any experience with works in this field. It's a little bit along the lines of Wittgenstein who asked in "Remarks on Color": What does a blind man mean when he says the sky is blue?
For all practical purposes (but based on some theoretical pondering), I am using "new media" in a very simplistic or na´ve way: anything which is run by something which is plugged into an electrical outlet (or generator) - "which is run" implies "time based", i.e. something which changes over times as an explicit and implicit condition/parameter - where the "time based" condition is an integral part of the work / concept / piece / production /intent / experience / perception. And since the term "new media" seems to have come up after media got more and more rooted in digital technology, mostly these days the definition not only includes electricity but also digital technology.
But, in all cases, I would never limit "new media" to "digital technology" for two reasons. One is, that analog electrical technology did change the paradigm of time-based art already a long time ago - and the introduction of formal and technical parameters implemented with electricity into the arts (gates, on-off, chaotic behavior, feedback, projection of images, loudspeakers etc.) is the basis for all digital technology and has had similar revolutionary consequences for the arts as digital technology during the past 50 years. And the second reason is that all digital signals have to be converted to analog signals before our senses/we can perceive them - we cannot create sense without this conversion.
Maybe "new media art" means "moving electrons" as material, condition, and consequence for artistic works which are "time-based" (as opposed to "static" (granting that nothing is static - but that is another issue)). Works in "new media" integrate the condition of "moving electrons" as tool and thus as material and thus as part of the experience.
Not very specific - but it does imply that "new media" is no genre and cannot be restricted to an explicit artistic position. But it does mean that when "new media" are used in an artistic production, the conditions of the "moving electrons" cannot be omitted. And this is not a technology based definition; on the contrary, it is actually an aesthetic postulate which liberates from the technological discussion in the sense that the technology which is part of a work is part of the work - and nothing just on its own.