Agreed with Kamen that the very fact that "transporters were down" establishes that some key centralized support resource was down, instead of the actual beaming machinery being hurt. Way too much such machinery aboard the E-E for all of it to get directly and uniformly hurt.
But what resource is that? If it's the usual targeting stuff and the tiny button is a beacon, then it isn't much different from a commbadge, and not even significantly more compact. No doubt most transporters are operated by "remote" in most circumstances - a commbadge suffices for controlling the whole process e.g. in DS9 where the runabouts don't have operators crewing a transporter console. The compact device from "Non Sequitur" no doubt is but another such remote, just like the "BoBW" armbands, with different situations calling for different numbers of push-buttons on the interface. But is the NEM button one of those as well?
The audience is tempted to think this is truly groundbreaking tech, what with being called "prototype" and all. But this is not an actual story requirement. Might be utterly humdrum instead: we'd get the same false impression that shoe heel -sized tracking devices are cutting edge in James Bond: Skyfall, even though they were cutting edge in a Bond movie three decades earlier, too.
Possibly Starfleet has always used "Emergency Transport Units", aka subcutaneous transponders aka pattern enhancers aka whatever. Or then those three are slighty different things and various packages hold between one to three of those functionalities in various sizes and shapes of casing. This Mk XCVIII button just combines good transponder range and power with adequate pattern enhancing at fairly good miniaturization level, but drops all user-selectability and reduces the interface to, well, a single button.
What other transporter resource could be involved besides targeting/remote control?
Timo Saloniemi